I voted on patching the tire from inside, but I'd have to say "it all depends".
If I hated the tires, looking for an excuse to get different ones, I'd say 'replace the tire' (and I'd probably be running over glass, nails and anything else I could find )
If they were brand new, and it was a tiny hole like a thorn would do, I'd use "Slime".
If they were worn a bit, but I couldn't quite afford new ones yet, then I'd patch, plug or tube them.