We live on a tiny suburban lot as well, and our front lawn is sacred ground. Our kids are 10, 9, and 7, and right now, them having a place to play is vastly more important than growing veggies on every inch. Our 20'x20' front lawn gets used by about 10 neighborhood kids every day as a sprinkler park, soccer field, badminton court, popsicle-eating venue, or safe-place-to-recover-when-they-skin-their-knees-riding-scooters.
I follow Paul's guidelines for lawn care
, which means no weedkillers or artificial fertilizers, just mowing with my reel mower, adding random organic stuff on it when available to improve the soil (like leaves or leftover potting soil) and a little water during the dry summer. It's probably 50% grass, 45% clover, 5% dandelions and other random stuff.
The other half of our front yard is a garden that's gradually being turned into a mini food-forest understory (too small and shaded by a big maple for any more trees to do well), and I've tried to make it as kid-friendly as possible, with lots of stepping stones, places for kids to plant and dig for worms and rollie-pollies, rocks and stumps and things. My kids do really well with it, but I have had quite a few experiences with neighborhood kids kind of running through pell-mell and stomping on baby plants, just because they don't know what's what. This is one of the main reasons I have not chosen to make the rest of the lawn more edible at this point - I want neighborhood kids to feel welcome here, not have me always asking them to stop trampling the strawberries. I would be insanely stressed out if I had a bunch of plants I really adore and have invested in getting accidentally mauled by my kids' friends.
Maybe you could put some sturdy, edible shrubs on the edges of the lawn area?
As far as ticks go, from what I've read, they mostly like to hang out in tall grasses and bushes, and they have to have a host to drop from in order to be in an area. We've gotten ticks from walking in open, unmowed fields with lots of deer, but we've never had any from a mowed lawn. Your area might be different though.