I tried to post before and Tribe crashed on me. Let's see if I remember...

The cave near San Ignacio is called Aktun Tunich Muknal, also called ATM. It is a bit pricey to get in but it fantastic. It's a beautiful cave, a great hike, and has some awesome Mayan pottery and remains of human sacrifices. It is like a living, nearly untouched museum and it's so awesome.

There is a set of ruins on the roast west from San ignacio to the border, called Xunantunich. You can pay a dollar or so to take the bus that leaves from SI, get off a few miles down the road, cross the river on the small ferry, and walk a mile or two. I packed myself a delicious lunch of plums, cheese and a sandwich and ate lunch at the ruins. it is small, but I had it all to myself. The tour groups tend to go in the morning when it is cooler at at noon, it was empty. There is another set of ruins right outside town but I did not go.

Definitely check out Tikal on the other side of the border. Go in the afternoon and buy a ticket. Last year at least when I was there, if you buy a ticket after 3pm you can come back the next day for free. I stayed late to watch the sun set, stayed in one of the hotels (you can also camp out at one of the hotel grounds), and went back the next day to catch some of the morning animals.