There isn't necessarily a limit, but the aftermath of traffic. If you do it right, mass transit will make it very easy for your sims to get into town and do their tourist thing. Getting them out is another story. Sims won't always leave the way they came. Some (usually med/high wealth hotel) will leave by Airport. Most (Attraction/Venue/Casino) will leave by car, which typically leads to crushing traffic gridlock.
But to more specifically answer your question, Tourists have an amount of money they will spend, and will spend it on the first thing they see when they enter your city. They go home when they run out of money or things to do.