How far can you drive an 1964 VW beetle?

A good rebuild should be fine for cross country driving. These cars are built to run long distances.

Make sure your cam and lifters match. Scat lifters won't last very long. Hopefully you have an original VW cam. These can be reground if yours is bad and will work with Bugpack, Engle, VW or UDO lifters. Deburr the cam to eliminate sharp edges on the lobes. Tolerances are extremely important. Also make sure you have all the original cooling tin including thermostat and flaps. The aftermarket cooling tins don't work as well. If possible upgrade to 1971 or later cooling tins. I recommend HVX mods for more longevity. Matching original carb and distributor will help reliability and longevity.

When driving, a valve lash check is important every 3,000 miles. Using leaner jets at higher altitude is optimal but not necessary.

Do that and enjoy your travels!

You're rebuilding it, so you know exactly what you have, a carbureted air cooled engine. Unlike typical modern ECU fuel injected cars, carburetors don't automatically adjust for altitude, so if you plan on driving across the country, you may need to rejet it leaner to handle the rocky mountain pass through Colorado/Utah. And then when you get back down into Nevada/Arizona/California you need to rejet it rich to avoid overheating in the desert heat.. Also the VW engines by design like frequent valve lash adjustment every 3000 miles or so. You aren't going to cross the country and back without at least one valve lash adjustment and oil change on the way. As long as you enjoy working on your car, you've got a car that you will need to work on several times to complete a cross country trip.

What makes you think there is a limit?

They weren't designed to not run, rather than to run!

They will last as long as they are maintained and/or repaired, so a lot of that will be up to you! I drove a 67 fastback cross country 4 times, and never had a problem.

You can drive to the end of the road if you have enough gas.

my experience, going beyond 60 mph is a task for the bug.