Hi Christine,
Solo travel by women is common in Costa Rica and as safe as anywhere. Many single women also move to Costa Rica. There are great expat communities down here that embrace people of all backgrounds – not couples only.
Just take the usual precautions about being out at night, sticking with licensed cabs, and stuff like that. Traveling by rental car is probably the most flexible way to get around but the driving here can be a bit intimidating at times, so that’s something to consider. There are also private shuttles that will get you door to door. And public buses that go just about everywhere in the country.
My suggestion would be to check out at least three but no more than five different areas during your trip. That way you’ll get a good sense of what a place is like and you have a basis for future trips and research.