Fishing is (essentially) free. Besides getting a license (or just risking it--which I wouldn't suggest), a small initial investment is all that's required (rod, line, hooks, bait, tackle box, etc.)
Once you have that, find a spot, cast your line, and chill out.
Did you know fishing is a sport? That's right. Even with the motor of the boat and all those fancy gadgets doing most of the heavy lifting... fishing is played on ESPN and there are tournaments for 6-figure prizes!
Fishing is also a good place to just chill and chat. You can do it from a boat or the shore, with minimal preparation and very inexpensive equipment. Find a body of water, find a date, find some fish!
Whether you want to consult Google or the Farmers' Almanac... or just take a stab in the dark, you should probably find out some simple specifics like "when do fish like to feed?what's the best bait to use and where to get it?" and "is there a time when we're NOT allowed to fish?"
That's a good place to start on when to go.
If you've been in your city for more than a few months, you should be aware of at least 1 place where there's water. Assuming you've been driving around with your eyes closed and ears shut... you can consult Google to figure out what a good spot to try is. There will be at least a few blogs related to fishing in your area and they'll have some suggestions. You may have to do a little bit of digging to find some good info, but it'll be worth it. A little bit of work now will lead to a fishing spot you can use all the time.