Ayutthaya, a historic capital city and world heritage site, is a short train ride and easy day trip from Hua Lamphong. Buy your ticket 1 day in advance. Most attractions are bounded between rivers though a few temples sit majestically across on the other side. Ferry’s take you across. You’ll find floating markets, tourist offices, and lots of temples in various conditions including Wat Chaiwatthanaram, a precursor to Cambodia’s Angkor Wat. There are even historic Dutch and Japanese settlements. Elephants can also be spotted around Phra Ram Park.
Songthaew, or local buses are the best way to get around. These distinctive trucks with 2 benches of seating drive fixed routes and are easy to flag down, hop on, ride as far as you want, then get off as you hand a 5 baht ($0.15) coin to the driver. Short ferry’s are the same price. I prefer them over Tuk Tuks which require tough negotiations and can be a waste of time.