You can get a 30 day extension in Thailand. Thus you only need to leave and re-enter once. Yes, you get the full 60 Days on re-entry, just be sure to have paper copies of MEV, and hand it to immigration officer, and check you were stamped in for 60 Days.
You can go Visa Exempt good for 45 days, soon to be reduced back to 30 days. Or get an E-Visa or a Multiple Entry E-Visa, good for 60 Days. On any of these you can get a 30 days extension.
The best beaches are on Koh Larn, an island just off the coast, a short ferry ride from Pattaya. Main land Pattaya, I like the A-One hotel chain. Also, LK Emerald Beach, in Naklua was great, on the beach, and one of the better be beaches in Pattaya.