1

If you just want to travel as long as possible on the least amount,why not look at Nicaragua or Guatemala? A lot cheaper than CR.....

If you want to go to CR because it interests you..then you could start in somewhere like Puerto Viejo or Cahuita.Easy to get to by bus from San Jose.

There are hostels where you can stay cheaply (in a dorm) and meet plenty of other travellers.

2

As per #1 if its all about budget then CR is not your best choice in the region but it does have plenty of cheap options. May-June is a good time as its shoulder season and the tourists will have dispersed somewhat meaning cheaper accommodation. Its not complicated- stay at a hostel in Alajeula for a couple of nights to get orientated when you arrive, catch the bus to Puerto Viejo on the carib coast and check into another hostel when you get there. Budget a minimum of $30 a day unless you are a teetotal bean eater who doesn't want to do anything....$40-$50 would be better...

3

1. you cannot use one "city" as a base and travel all around. you can do day trips from an area, but the best thing to do is to plan on several locations, depending on the amount of time you are in the country.

2. for hostels, google or use hostelworld

3. do some more research and decide what interests you then pick an area.

4. puerto viejo and the caribbean coast is a good start. here's a good source of information http://www.puertoviejosatellite.com

some more information: http://www.thebusschedule.com/cr/
distances and travel times: http://www.yourtravelmap.com

5. for a 1-week stay figure 2-3 locations, depending on your interests and what time your flight arrives/leaves - you may need to spend your first/last night somewhere near the airport, which is in alajuela and not san jose.

4

I would like to see how long I can explore on the least amount. You are not the first to explore the possibilities Clay. Others have gone before and lived the life. Don't let any of the naysayers dissuade you.
http://cache.deadspin.com/assets/images/11/2012/01/f1e8b154e1f0dbfeec0afe6c2c760997.jpg

5

as jirijiri wrote - don't let any of the naysayers dissuade you. you can find inexpensive accommodations - sometimes just a hammock at a hostel or a tent on the grounds of a small hotel or "cabinas." homestays are all inexpensive and you get the bonus of staying with a friendly costa rican family. wherever you go, just ask around.

if you speak spanish, this will be very helpful in finding inexpensive places to stay. word-of-mouth is the best way to do this and asking waitpersons, taxi drivers, bartenders, bank guards will often produce a welcome surprise for little money.

on the caribbean coast, most people speak english so that will be helpful to you there. make sure people understand you are not a rich gringo. you might even put together a little dialogue -- something like -- you are trying to see just how little you can spend in costa rica as a tourist and still survive and have a good time. once you start talking to people, you will find them to be very helpful.