What part of Bangkok/Koh Phangan/Chiang Mai to stay in?

In Bangkok I would choose a hotel near the Skytrain. The Skytrain can take you around town cheap and easy. You might want to check out some hotels in the Sukhumvit Road area. In this area there are many restaurants, travel agencies for tours, street vendors, malls and a lively nightlife. Hotels in many price ranges.

Swiss Park, Grand Business Inn (off Soi 2,) Fortuna Hotel (Soi 5) are a few that come to mind. Check out the Asia Hotel, it is not directly close to nightlife but it is directly on a Skytrain stop making it easy to get to many places (until the Skytrain stops running and you have to switch to a cheap meter taxi.)

Basic, cheap air conditioned hotel rooms with hot water and private toilet start arund 600 baht, a hotel room in the 1200 baht o 1600 baht isn't too bad.

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In Chiang Mai I have used the Montri Hotel on 2-6 Ratchadamnoen Road, directly across from the Thapae Gate. This location has many restaurants, travel agents, a cooking schoo or two, internet shops and several Seven Eleven type stores. Easy walk to night market. The best room that the hotel offers will be less than the $75 you want to spend (air conditioned room, hot water, private toilet, security box, cable TV and maid service.)

Good luck.

Chiang Mai Thai House has everything you are looking for - except that breakfast is not included in the tariff (but you can buy it yourself at the restaurant!). 550 - 1150 baht per night.

Ko Pha Ngan : Thong Nai Pan is not completely isolated but it is c.15km from Thong Sala, on a dirt road (rough at times) for at least half the way. If you want to be less isolated but still in a quiet, relaxed location, you might want to look at Hat Yao bay on the west coast which has several nice resorts, a good beach, and is reached by paved road so is more accessible to Thong Sala etc.

Plenty of places reviewed here: http://www.travelfish.org/country/thailand

Personally, I wouldn't be without a pool in the tropical heat, except of course at the beach.

Look for the Sunday market from Tha Phae Gate. I don't care for the tourist trap of the Night Bazaar. I would rather walk along the east side of the river to the places with live music. Cabin, Riverside etc.

See Chanchao's Chiang Mai food reviews and Travel menu: http://chanchao.fotopages.com/

See the Bangkok rail map. BTS=skytrain; MRT= subway
http://www.guidetothailand.com/maps-thailand/map-bangkok-subway-skytrain.htm
I like to be on the skytrain line that goes to the river. On the map see National Stadium, BTS Main Station at Siam Square, Jim Thompsons house. Not only is this the start of the river line, you also have the fast cheap canal boats.

You may find hundreds of posts on Bangkok hotels in the SEARCH. I have posted many times how I find nothing of interest on Sukhumvit tourist ghetto. I recommend the old city near the sights, or the skytrain from the river through Silom to Siam at the furthest.

Siam Square area hotels: http://www.travelfish.org/accommodation/thailand/bangkok_and_surrounds/bangkok/siam_square_and_surrounds/all

I often stay in this area and for entertainment go the opposite direction from Sukhumvit. For example, to the Victory Monument Plazza and the Saxaphone Pub.

The river area is the main sights of interest: http://bangkok.sawadee.com/canals.htm

In Koh Phangan I stayed at the Grand Sea Resort. It is just outside of Thong Sala, it is about a 20 min walk to the main town. We thought it was a great location because at night we could walk to the food market for dinner or to do some shopping. It was basic accommodation with an awesome pool and relaxed atmosphere. They also have kayaks to rent and travel to this spooky island across the way. The restaurant was great and cheap. Duncan is the guy that runs the place and he was very accommodating and made us feel welcome. We went for the full moon party, so we preferred it to the Had Rin area because is wasn't touristy and we could hang out with the locals. We also rented a scooter and would travel around the island (except to Had Rin because the road is very twisty). One of our favorite beaches was Haad Yao.

In Bangkok, we stayed at Lamphu House. Again basic, but very clean. It has a relaxing court yard and is quiet. This place again had a great location within Bangkok. The taxis are so cheap and you can walk or take the river boat anywhere.

In Chiang Mai we splurged and stayed at the thai lana villa which is a residence at the four seasons, but for way less. It was very awesome. The most beautiful place I have ever seen. If you want to treat yourself stay here. I think it's about 250 a night.

250 whats?

Just got back from Thailand. I stayed at the JW Marriott (not sure what part of town it was in). I can't quote you on how much it is for a night, but it is on the pricy side (not sure how much you want to pay). They had a river taxi that would take you to the sky train and where there are public river taxis. It was quite easy/cheap to take the sky train and river taxis once we were there.

"...They had a river taxi..."

I think lizzy is confused. Marriot is on Sukhumvit far from the river and sightseeing. Unless there is another one on the river.
Also it is 2 or 3 times your budget.
A river hotel would be wonderful. Don't know the prices though.