Budget tour to Taiwan, free and easy, relax and no rush, any suggestion?

I was just being retrenched from an US company. Before looking for a job or planning something to do, I will like to go for a budget tour together with my husband. My first destination is Taiwan. Can someone share with me the best plan in tour around Taiwan at cheapest cost? We plan to go 2 weeks, relax and no rush.

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2. Taiwan is small and it's easy to get around. Apart from Taipei city, and if you're a nature person, I would suggest Hualien. I'm not sure if it will be too hot at that time to go on the hiking trails and stuff. But I took my partner, who had never been to Taiwan at that time, and he said that Hualien is his favourite city. There are TONS to do in Taipei and it's so convenient because the MRT takes you to a lot of them. I love, love landscapes and scenery and such and if you do, too, this is great for it. Here's the wikipage for it: http://wikitravel.org/en/Danshui There is this huge bridge that people like to take pictures from and the view is amazing. There are some good food stands there. When I went there were some eclectic live bands. It fit well because it was of a woman playing an acoustic guitar and another was a man who was playing jazz on the keyboard. It was nice. You can also take a boat ride, I believe. Night Markets! Cheap, plentiful and full of people. Try as many snacks as you can. I know that stinky tofu is REALLY stinky, but hey, you might like it. There were also awesome fried chicken, ice cream, popcorn, Crepes with ANYTHING! (sweets to salts as in fruit or beef. haha). The biggest one is in Shilin: http://en.wikipedia.org/wiki/Shilin_Night_Market pretty convenient because you can take the MRT.
3. All peaceful and non-smoking international travelers are welcome to stay at PROF. LEE'S HOSPITALITY APARTMENT SUITE! Prof. Lee is not doing business. He is a part-time university teacher. He did postgraduate studies in Texas, California, New York, and Scotland before. He likes to help peaceful and non-smoking international travelers spend less but enjoy more. He promises you a very safe and pleasant stay at his place. He can give you useful tourist and transport information. If you do not have a tour itinerary in Taiwan, he can help you make a very good one according to your interest. He will show you around Taipei if you do not know Chinese. Just bring your passport, visa, airplane ticket, clothing and towels, and travel budget, and you will have a happy time in Taiwan.
4. If you want to relax, Hualien and Taidong have some of the best scenery and nature spots in Taiwan. Probably the best bet for that is to take the North East Coast railway- its cheap and shows the gems of Taiwan. Yangmingshan is a volcanic national park nearby Taipei that has a good trail system to wander on. You can take a bus or taxi to get to the trail head. The public bus system should get you there alright. There is increasingly better signage in English on the buses but I cant testify from personal experience- I use a car, being the environmental criminal that I am. Also nearby Taipei and worth a wander is Jiu-Fen (Joe-Fen) township, a precariously placed former mining town that has redesigned itself as a tourist spot. Yes its a bit of a tourist trap, but it does have some sweeping views of the ocean and mountain, as well as some nice teahouses you can pay some $ to sit and drink and relax at, as well as a lot of gift shops to drop your savings on... I suspect that you wont want to do that, but its got some ok stuff there. In Hualien city you can find a shuttle tour bus at almost any hotel or guesthouse you stay at that can get you out on day trips to the nearby destinations. Taroko is ok, the East Rift Valley is a gem that is worth seeing. There are bike trails in Guanshan between Hualien and Taidong that are beautiful and worth seeing. Bikes are easy to rent and the views are excellent. Its hard for the hordes to access this area- its a good spot to spend a saturday or sunday on in the middle leg. I think there is a railroad connection to that area. But you may need to get that checked out. Kenting National Park is worth seeing, but I recommend doing this on a weekday. The horde will be out on the weekends, making nice places not so nice and creating lineups and parking problems. To get to Kenting you are best off taking a bus if you dont rent a car. ---(Cars give you the freedom to go at your own rate-- but are expensive AND people here drive like psychotic maniacs on K. Which probably many actually are. The rules of traffic are the exact opposite to what you learned in North America so dont drive unless you have experienced living in developing countries before.Traffic is not a joke, I know most people who visit/work here who die... its due to traffic accidents.) Guest houses are probably the best quality idea for saving money. BUT you will run into language problems and have a lot of hassle finding the best ones... so using hotels or just walking down main tourist drags and finding spots that look good is a viable option if you go to Kenting or Hualien. If you want to Camp I recommend spending a night or two at Hsi-Ti-Ping Campsite between Hualien and Taidong. This will require your using a car however. You can rent tents and sleeping bags there... the english signage is passable, you probably can find someone there and use sign language in the worst case situation... Hsi-Ti_ping is basically a big rock formation on the beach. Its a good quiet location away from the madness... but it probably gets a little mad on weekends like most spots here. If you get to Taidong city, you probably are best off getting a tour to see Green Island. You can take the vomit comet ferry to get there and the guest houses generally include your breakfast, a scooter rental and a snorkel trip... (warning- no visors on free scooter helmets =bug teeth -yech.) Its pretty good. The guest houses on Green Island will often send a van to pick you up from the train station in Taidong, that brings you to the pier to ride the vomit comet. then you arrive and get your scooter and are led to the guesthouse. from there you can tour around on the scooter at your own leisure. The island is small, you can traverse the whole island in less than 2 hours on a scooter. Kaosiung Love River. Yes it sounds like the OTHER love river doesnt it. It used to smell equally bad but is one of the rare environmental sucesses due to Frank Hsieh's fine leadership during his time there. Check it out at night. This is a good weekend stop - it will be crowded no matter what but the hustle and bustle of Kaosiung can be captured here. (bus from Kenting to here) Tainan's red Castle- a good location to see some history of Portugese colonization in Taiwan. (Train to bus accessible) Alishan- wake up with the hordes and see the sunrise. Or just take the train up at your own timing and wander down. Its all beautiful. (train accessible.) SunMoon Lake- a bit yicky of late due to overdevelopment and the opening up for Chinese tourist buses to come. It still is beautiful but the banks that used to have green areas are disappearing quickly. Still, the mist over the water and mountains can still manage to take your breath away. But the annoying boat ride touts can cool any misplaced romantic mood fast. SunMoon = overdeveloped trap... but worth seeing if you have a day to blow. I ran out of space. sigh.
5. depends what kind of person u are, like to shop, likes cultural stuff, or just a nature person