I was in all three places a few months ago.
Chiang Rai - I was only here for one night and I stayed in the Wiang Inn hotel which is around the corner from the bus station. Nice place and excellent breakfast. There was 3 of us and the room cost about €30 per night if I recall. Went to the night market which was quite good and on to a bowling alley which is about 20 mins on a tuk tuk. Bowling Alley was a cool place as it sold beer and was quite lively.
Krabi - Flew here from Bangkok and got a taxi for about €10 to Aonang and stayed in a nice place called Srusuksarn Resort which was quite expensive at about maybe €60 per night. Aonang is a nice place with maybe a 1.5m stretch of bars, restaurants and shops. Very relaxed place. Stayed here for about 3 nights but was quite ill so didn't get up to much. Went kayaking one day and this was quite cool - for about €10 - 15 well worth it for a half day.
Got a boat over to Phi Phi (and stayed for a few nights) from Krabi that takes about 3 hrs I think. Great views on the way over. Phi Phi is a nice enough place itself but it's getting out to snorkel and dive that is great in the area. Went on a half-day snorkel trip for about €15 that was excellent. Visited the monkey island and "the beach" on the trip. Lunch included and very relaxing on the boat. It's a must if you go to Phi Phi.
Didn't enjoy the diving as much as not a great swimmer and couldn't settle but views were still great - saw some sharks and the usual. A guy from Dunshaughlin actually has a diving school in Phi Phi and he has a couple of great instructors.
Bangkok - If you like temples you can fill you boots here. They weren't for me - all looked the same to me and a bit tacky for me. Still the Grand Palace is worth a visit. Weekend market is huge and worth a visit - can't recall the name of it but you get off the skytrain and a place called Mo Chi (sp). Went to the kickboxing in one of the stadiums and it was quite good. Not sure which stadium but if you go don't bother with the VIP tickets as the arena was not that big and you have a good view from everywhere. Only the tourists get roped in to buying the VIP tickets.
Stayed in a Viengtai Hotel(maybe €30 for night from what I recall) in Bangkok which is just off Ko San Road (main backpaker area and very very lively). I spent a few hundread € before I left Ireland buying cloths and packing bag. I wouldn't do it again if heading back to Bk. You can get t-shirts for €3 on Ko San Road, shorts €5 and everything else you want is also available including student cards and a degree from Trinity.
Went up the Patpong (Red Light) one night as there is a market right in the middle of all the action. Good place for a beer and watching the world go by.
That's all I can think of for now. If anyone mentions voglee walk away - scam.
Hope this helps.
If flying around check out Thai airlines and bangkok airlines for best prices I could see.
For accomodation see
www.sawadee.com