Don't forget to bear in mind costs of going on from Bangkok if you are going to Phuket or Pattaya.
For Pattaya you land at Bangkok and then either catch a bus or a taxi. Bus is obviously cheaper but also more hassle and longer, about 4 hours+ as you have to go from the airport by bus to the main bus station and then catch another bus from there. Taxis are available at the airport and will drive you striahgt to Pattaya. You could use the limousine service (I usually do) which cost 3,600baht for a return trip last time I was there, this is roughly $90. If you are alone it is expensive, but if there is 2/3 of you, then if will be cheaper per head. This is the maximum you should pay, it will include all tolls and you get driven in a nice comfortable car. At the other end of the scale, you can take a meter-taxi from the rank, not all will goto Pattaya so don't be put off if the first one says "no". These cars are less comfortable, but OK as a rule. They have a meter but will ask for a fare and switch the meter off, this is normal. With these taxis you can expect to pay around 1,000 - 1,200baht for a one-way journey and unless you state it during cost negotiations, you will have to pay the tolls. Last time it was 130baht in total if memory serves me right, so not too much. Try to avoid them agreeing 1,200baht for the journey and then saying "1,500baht and I pay toll". I got done first time by that one, I ended up paying 2,500baht for a one-way taxi ride (including tolls) to Pattaya and it wasn't even from the airport, it was from central Bangkok which is even closer !!
I don't know what the fares are for the bus, but I can't imagine that it will be more than 500baht for the bus to the main bus station and the second bus to Pattaya. I seem to recall there being information on the web somewhere, so maybe a search will give you current prices.
For Phuket, you can catch the train but it takes almost 24hours to get there. It's too far for a taxi and what you would pay would be about the same as the airfare. So flying is the best option. Most expensive way is Business Class with Thai Air which will set you back around $200 for a return trip, you can expect to pay around half that for Economy with the same airline. There are other airlines that you could try, but I don't know about the prices for those.
www.nokair.com is one I know of, there are other threads on here that should give details about which airlines and there websites, again try the search facility on the forum and see what it brings up.
Once you get to Phuket airport, you will then need to get a taxi to wherever you are staying. There is a thread about this that would be a good idea to read, although don't be put off by it, after having re-read it myself I think some of the comments make the situation seem worse than it is.
www.phuket-info.com/forums/showthread.php?t=6931
If your hotel offers a taxi service, it would be an idea to give this serious thought no matter whether you are staying in Pattaya or Phuket. They usually charge reasonable rates and it means that after your long flight, you walk out of the airport straight in to a nice car and you don't have to worry about haggling, booking, getting one bus and then another etc.
Good luck
Diz