you may want to book your first night in bangkok at least, you will be tired when you arrive- get a taxi from the airport by going to the taxi stand. i think it is outside door 7(?) but others will know more precisely. should cost about 400B for the taxi.
take the overnight train up to chiang mai. you can buy a ticket in advance if you want and have it delivered to your hotel in Bangkok, or buy this when you get there (advance purchase will save some time later though). so much to do in chiang mai and so much cheaper than the southern beaches. elephant riding galore (see
Thai Elephant Conservation Center along with many other camps), trekking, touring, flight of the gibbon (zip lines), white water cooking school etc etc the possibilities are endless. My husband has been in CM for 4 weeks lucky thing on sabbatical and has done a few organised courses: a weeks tai chi staying in university housing, a week at massage school and has just left for 2 weeks yoga in a lahu hill tribe. I'm green with envy, but join him next week with our daughter. He has been staying at lanna house (which he liked), banilah (wasn't very enthusiastic about this) and rainforest inn (his new favourite)
When i arrive we will move to the centara, a world away in price at £30 for 2 with breakfast!. My plan is the zoo, they have pandas, doi suthep, a day touring with paul collins tuktuk tours, flight of the gibbon and a day on quad bikes in the jungle. Then we fly to phuket airport (would take forever by train) and head north to khao lak (orchid resort). this could be too quiet for you but we love it. there are, however, more lively areas of khao lak. If funds are running low, you might want to consider KL over some of the other beach areas as it is still much cheaper than phuket, samui etc etc. The orchid is a little remote but there are other parts, like bangniang with more going on within walking distance. there are good reports of cousin resort and nang thong resort.
For busy, busy, see phuket, especially patong. samui is also fun but cannot comment on other islands.
Personally, I would to this without a tour; we took a 6 night tour on our first trip, and although we did see a lot and learn a lot, we also felt dissatisfied at the pace, accomodation and meals. Just organise it yourselves. spend time exploring chiang mai, or go up to mae hong song. research a few day trips you want to do, and book them when you get there. consider a 2 night trek, with a third day spent white water rafting for example. Spend a day with elephants (or sign up for 1 or 2 nights at an elephant camp). We find on each trip we are spending less and less time in the south, and more time in the north.
have a great time. with 3 of you, consider serviced apartments instead of hotels they will be better value.