Whats the cheapest way to travel there(from Bangkok) and how long will the journey take?
and is it a good plan to go to Pattaya early in the morning and come back in the evening.
Best way is taxi. Price is negotiable, but ranges from 1,200 to 1,500 baht one way. Flag down a metered taxi instead of going to the 'limo services' in Sukhumvit Soi 5.
Taking a bus from Ekamai Bus Station will cost you less than 200 baht.
It takes me less than two hours to get from Bangkok to Rayong, but in taxi, Pattaya is probably almost two hours drive from Bangkok (more if by bus). So it doesn't make sense to go for a day and nobody goes to Pattaya for the beach life. If you want to go, go for the night life, i.e., return in morning rather than coming back in the evening.
