The dates you travel to Puerto Rico will have a big impact on costs. Tourist season is officially between December and April, when Americans fly down to escape the colder Northern climates. Because fewer Americans go between May to November, you're more likely to find deals on everything from flights to lodging to tours. However, note that these months correspond with peak hurricane season, so trips during these months are more likely to be disrupted by nature.
Lodging in San Juan doesn't have to be expensive. Hostels in San Juan start at $15 per person per night at the San Juan Hostel and $21 per person per night at the Fortaleza Guest House. Both have kitchens, so if you want to buy and cook your own food you can do so cheaply. Both have shared bathrooms.
Food in San Juan may be more expensive than in other places on the island, but you can still eat cheaply. Try Panadería España Repostería for soup, tapas and sandwiches (between $4 and $8). Cielito Lindo has main courses starting at $5. Repostería Kassalta has breakfasts starting at $3.50 and sandwiches cost between $4.50 and $6. El Hamburger has--surprise--hamburgers for $3.50. There are also the common American fast food franchises, but with family restaurants this cheap you may as well eat like a local.
If you want to get out of San Juan, cheap flights can be found from San Juan to Culebra, a tiny island to the east of the main island. Here, you can camp on the magnificent white-sand beaches for $20 per night. Cheap food can be found in the town grocery store, or you can buy food from local vendors. It is possible to have everything you need for $30 per day.