Ideas for short San Juan-area trips

I'm going to San Juan for a wedding in mid-March, and I have the time to spend an extra couple days there on my own after the wedding. Sunday night I already have accommodations in San Juan so I'll see the city for the day on Sunday. My main question, however, is whether I should leave Monday or stay through Tuesday morning (I have to leave by then at the latest.) Is there enough to do in San Juan for two days? Or are there any day trips I could do on Monday (or overnight trips as long as I could get back by Tuesday mid-day)? I won't have a car, so I would need to be able to get around via public transportation or some sort of arranged trip.

Thanks so much for any advice! Reply to this