agree with hinhinmummy, there are many places and things to do, also can consider JJ Market as there is a "pet section" with lots of puppies, kittens, rabbits and hamsters etc. But it is really HOT and stuffy there.
safari world is really nice and you can feed the giraffes!
also, my son said the best part was actually swimming at the pool!
agree with Busybc, bts (sky train) very easy and fast. better than taxi because traffic is very bad on the road.
I don't know the tours now, but they used to go to all the snake farms and places not so interesting to me.
for hotels, the Intercontinental is quite good, I like their pool and the place is right next to BTS station, no need to carry your baby for so long. Shangri-La is also good, but a bit more expensive, look out for promotions ah. It is quite far at the end of the BTS line, (but still easy to get to the town centre) but very nice hotel, pool is a bit small. The Swissotel Nailert park has a very nice swimming pool, but you have to walk 8-10 minutes to a nearby BTS station.
many of the hotels don't need you to pay for extra bed for kids, please check with them, otherwise the beds are usually very big, enough for you and the bb.
if you go to safari, you need to take a taxi or rent a car, last time I went I rent a car to the safari, more expensive than you take a taxi but quite reliable, if you need the contact, please pm me.