Don't have stuff to steal and they won't steal it. Use ATMs when you get down there during daytime hours a few times, but leave all your ATM cards and passport and some emergency US dollars in a hotel safe as much as possible. When walking around town have about $50 in local currency and one visa card (mastercard doesn't always work south of the border I have noticed), $20 or less of small bills in local currency in a different stash away from your main roll such in a sock (and hope you never need to use them), and a drivers license and copy of your passport on you. Don't wear a watch; if you can't live without knowing the time buy a $5 watch, bust off the armbands, and carry what is left in your pocket. Minimal jewelry and keep any maps you must carry discrete. Dress like a local which means modest button up shirt or polo shirt, jeans and tennis shoes or casual black shoes. Locals in most areas of Latin America don't wear shorts except in the resort beach towns. If all else fails, just look around day one and go do some modest shopping day two. Yes I know, can't go to the Del Rey like this, but use common sense there if you go because everyone says working girls are the best at not just "relieving" you, but also your money.
Not meant to scare you, but just guidance. If you look like a broke tourist, or even better yet, a modest local, no one bothers you and your chances of robbery are almost none. Sometimes you can't help it because of your appearance, but lots of light skinned people in CR so anyone can blend in somewhat. You will know you are doing it right when people start asking you questions in Spanish like you are a local. I have made 10 trips to Mexico City, what everyone calls the most dangerous city around without one problem. I have been in Colombia twice, once again no problems. San Jose is a cakewalk compared to those two in terms of crime and ease of looking like you belong since light skinned locals aren't uncommon, just do a little thinking about it beforehand and you shouldn't even have to worry.