I have been a few times to Siam City Water Park. A Taxi from say Silom would be in the vicinity of 300B with tolls. Several bus options as well, including one from Silom, you need a Bangkok Bus Map: 115,151,26,60,168,501,519.
The entrance fee for the Amusement Park and the Water Park can be separate or combined. There are several different confusing package fee options. The rides in the amusement (thrill rides) section are on an individual ticket system but you can pay cash as well inside the park. I am pretty sure there's duel farang/thai pricing but if you have a Thai DL you pay Thai.
I can't recall what I paid. I took the BF's family and there were a lot of them and I don't recall it costing much. We had some discount coupons from somewhere and food in the park was also not expensive.
Most Thai families come only for the water park. There are the usual water slides and large pools. Weekends and school holidays it gets packed with families. It's not a big farang attraction but there's the occasional farang here and there including some PLU and once I saw a gaggle of lady-boys. There would be no problem going with a BF/BS or a group of Thai boys.
The rides are comparable with Dream World but I might give Dream World an edge on the quality of the park and rides but no water park.
Siam Park City
You can print the map which might help a taxi driver find the place--good luck. It might be better to asks if he knows where it is and if not find another taxi.