It is quite possible to travel from the US to Costa Rica via bus. Bus prices begin to drop dramatically when you leave the US and enter Mexico. It's also a great way to meet a lot of friendly local people. Disadvantages are that buses can be quite crowded (especiallly if you are over 6' tall), schedules can be somewhat erratic, and some drivers are rather macho in their driving habits.
The train is a really cool way to go. Although written quite a few years ago, Paul Theroux's Patagonia Express is a great book on riding trains through Latin America. I note that the reviews on the Amazon website point out that Theroux is a cranky traveler - I liked the book anyway.
Although challenging, it can be done. I hitchhiked from Alaska to Peru when I got out of high school. The usual cavets apply - this is only for the very adventurous, and is not recommmended for women traveling alone.
Melia Cariari (Near the airport, $75-$250) - Well known tourist hotel near the airport. Nice pool (note: check and see if it is open, they are remodeling), nice rooms, near shopping center. Shop on Travelocity or other sites - I have paid as little as $75 a night, at the same time others were paying $150.
Hotel Martino (Near the airport/Alajeula, $90-$175) - One of my favorite hotels near the airport. Across the street from the zoo. Awesome pool, nice restaurant. Keep an eye on your food and drink bill - it adds up fast. Again, check Travelocity or other online booking sites for discount prices.
Hampton Inn (Closest to Airport, $99) - Very close to the airport and rental cars. If I was not trying to save money and needed to spend the night near the airport and catch a flight in the morning, I'd probably stay here. Seems like it's always $99 - hard to get a discount.
Hotel Hemingway (San Jose, $37) - Inexpensive, friendly. No A/C.
Hotel Del Rey (San Jose, $55) - Good location close to downtown, good security, reasonable rates, free parking. Free Internet access. I was able to log on their WiFi network from my room last time I was there as well! Fishermen's hangout, not for those seeking solitude.
Hotel Don Carlos (San Jose, $55-$65) - One of my favorite hotels in San Jose. Great gift shop, good security, free parking. Recommended for couples and people who want a quieter place off the main drag. Free Internet access. Run by a family of attorneys - free legal consultation.
Hotel California (Quepos/Manual Antonio, $70-$120) - Nice hotel just before Manual Antonio park. Pool, air conditioning, restaurant. You can sometimes bargain at the desk for lower rates, especially in the off season.