Locate studs, conduits, cables, etc from the inside garage wall using a "stud finder" (which finds anything in the walls, not just studs), available at Home Depot and hardware stores for about $9.95. A very good investment, and it comes with instructions that will answer all your questions about how to use it.
Once you've found a place that's clear of studs, wiring, pipes, and everything else: If your garage wall exterior surface is just wooden shingles or something that can be drilled using an ordinary drill bit, by all means feel free to drill from the inside to the outside, using a drill bit sufficiently long to cover the distance. However, if your siding is stucco, brick, cement, plaster or something requiring a masonry bit, you're better off drilling from the outside to inside, so the masonry bit tackles the hard surface first. In this case, once you've cleared the masonry and are in air or softer materials, you can change from the masonry bit to a regular drill bit and continue drilling from the outside until you're all the way through.
If you're running a lot of cables through the same hole, I'd recommend making the hole large enough for a PVC pipe of sufficient diameter to pass all the cables through -- maybe 1.5" or 2.0", or whatever it takes. PVC pipe is surely cheap enough, and easy to cut using an ordinary coping saw. What I do in this situation is cement a PVC "elbow" fitting to the PVC pipe on the "outside" end of the pipe, push the straight part of the pipe through the wall until I hit the elbow, rotate the pipe so the elbow faces "down," and then use RTV caulking compound to seal the pipe against the outside wall. Let that compound cure until it's strong. This provides a rain-resistant cable entrance (since the elbow faces down, and rain doesn't go uphill!).
Once you've run all the cables you're going to run through the PVC, fill any gaps from the outside with insulating material stuffed firmly into the elbow, to keep out bugs and critters. If you have insulation-eating critters, you can use putty or something more critter-resistant; although I prefer soft insulating material, so it can easily be pulled back out for future servicing.
For just one feedline and one ground line, I wouldn't bother with the PVC -- it requires drilling a much larger hole than necessary. For RG213/U-sized coaxial cable, only a 7/16" diameter hole is required. The cable will occupy almost all of that hole, leaving very little space for anything to enter the garage other than the cable itself, although some RTV caulking is still a good idea.
This isn't a "big step," Mike. I've drilled dozens of holes in every home I've ever owned (lots of them!), and just recently drilled 12 1/2" holes in my new home (stucco exterior, masonry bit required for every hole) to bring in cables to the shack. Yawn. It's not a big deal. Anything you do can be patched back up when you sell the house.
73 de Steve WB2WIK/6