I just went with my 1 year old (am back yesterday, jetlagged today but what a fabulous trip we had)! We flew BA direct to BKK, it was better for us with a small child as we could use the travel seat/bassinet at the bulkhead seats. My son was too big for the bassinet but the BA travel seat is a bit like a bouncer that fits children up to 2, so he slept well and travelled comfortably. I've done the 7+7 hours flights via the Middle East a few times before; I have to say I much preferred going direct this time and found I adjusted better to the time zone change. I'm not doing so well on the way back, I've been up since 3am...!
Chaweng is not very good for kids, too smelly, dirty in the daytime and lewd at night. Good for a kidfree night out though! Bophut is where we stayed this time. We stayed in the Mantra hotel (up in the hills, fabulous views and lovely rooms but remote and difficult to get around anywhere) and the Bandara (rooms not as nice as the Mantra but lovely location and good facilities). Fisherman's village is a short walk away and there's a night fair on Friday nights when it is closed to vehicle traffic. Renting a car isn't really worth it, it costs about £20-£25 a day, but you can hire it as a one-off for day trips easily enough. They don't really do car seats though...
I have been really lucky too in knowing a good nanny/babysitting service to use when my husband and I wanted some kid-free time. I had been to Thailand many times before having kids, and while I was at home, pregnant I saw on Facebook that one of my Thai friends, who lives in Samui is married to a Dutchman, had set up a Nanny agency. I thought, oh brilliant, I know Pim well and she's a careful and kind person, I'd definitely trust her with my child when I go again.
It's been better than expected, actually, all of her nannies are trained to a Western standard - they write down details of all feeding, naps, activities, nappy changes just as my nursery at home does - AND they all have first aid certs and swimming certs so they can take your child to the hotel pool etc. We ended up booking a few more days' service than we had planned to, but we were very confident with the nanny we got and it was nice to be a bit more carefree on hols. She was fab, I came back early to the hotel room and saw her playing with my son through the window before they spotted me, he was laughing his little heart out, and when we left she had tears in her eyes saying goodbye to him.
(I don't really know what the rules on advertising are, or if I can mention the business name outright, so to steer clear I'll say you can PM me if you think you might want the website address or contact details for Pim. They have a daily rate and an hourly rate; these are the same whether day nannying or night-time babysitting. The cost to me was about the same daily rate as my nursery or less than the babysitting service I use in London.)