You could set up a user-place relationship and simply increment the number of check-ins for that place, then periodically correct the number, subtracting old ones which no longer count. Or look at the entire history only if there is a chance of getting a badge based on this number and otherwise just increment it. For badges for the total number of check-ins this is even easier, since no recalculation is necessary.

I suppose if your CPU load is not too high you could even run background processes to monitor "near-badge" status for all users with high enough frequency. This you could really get wild with: people with most number of recent check-ins should get scanned first and of course this list should be updated as a separate entity so it stays small and always in memory.