The classic is peonies. In snow country, there is a great deal to be said for something that disappears into safety during the winter.

How about some kind of small attractive ornamental grasses? Any suggestions? For a 50 ft driveway (100 ft of border!) wouldn't grasses be inexpensive solution?

Ornamental grasses are great for this. You can do masses of different grasses. Little Bunny Fountain Grass is a great one. I like Morning Light Maiden Grass for larger accents a few feet back. Elijah Blue Fescue is nice also, but I find it is inconsistent in my area. They are also forgiving to those occasional stray tires.

Liriope is mostly ignored by deer here and is evergreen. Carex, too. In snow country, I don't think I'd do boxwood. It'd take years to repair any damage done by accidentally going over the edge in winter. I had to put in aluminum posts to protect my plantings near the street.