This may seem really strange to many of you, but our June date was a Barnes & Noble gift card which were to spend on a fun book to read together. Since we both love fantasy novels, we found a fun one about dwarves. It is super silly, but lots of fun to read it. We read a little bit each night before we go to bed. It's the date that keeps on giving! We are both enjoying it greatly, plus when we went to go find B&N it was a good chance to explore our new town! It was in a big mall which was fun to look around, and we found some yummy restaurants which another big plus. So, overall, we had a very successful date day :)
The other book we bought (our gift card was $20, so we got two cheaper books) was the full collection of Grimm's Fairy Tales which was on sale, but is a really cool hardcover version that is a great display on our shelf as well.
Anyway, hope this provides some inspiration for you!
Look here to see our other dates for the first year of our marriage :)