well....you can visit her town and her yours.....if you neglect your town....you just get weeds growing and stuff.....you can always swap fruits, which is what you'd want to go online for, so that you have a different variety of fruit trees growing, ALSO, you unlock the 'mall' type store when either you or her (vice versa) buy something from each other's town store at a certain point. You'd have to look it up on gamefaqs.com
Hmmm.....as for games you can play together......you might want to try pokemon? you can battle each other, or dig in the tunnels together....
depends on if you want co-op or battle type.
There aren't that many co-op (if any) games, but battle type there's quite a bit