I suggest that you stay at the Dynasty Inn (next to Nana Plaza) and then try their sister hotel in Pattaya. Both are good hotels (each costs around 1000 Baht per night).
They do not charge for the transfer to Pattaya, but charge 400 Baht for the return trip to Bangkok (at least they did a year and a half ago when I last used this service).
If you don't wish to tie yourself to this hotel you can get a taxi to Pattaya for 1000 Baht, it will also cost this for the return.
