Anything nice driving distance from OSL?
+1 about being very expensive, bear that in mind.
Around Oslo, if you want to go to the old synagogue you got to register a month in advance and they do a background check. (Just from what I saw, I personally didn't go)
I didn't stay around Oslo because from what I looked into there really wasn't a lot to do there, so wasn't worth it to hang out in that area, what there is
The Folk Museum in Oslo is nice to visit, and there’s a Viking museum not far from there.
I would highly suggest, you take the train from oslo to bergen, you'll get the most amazing ride of your life, takes about 7 hours, it's usually 100$ for a one way ticket.