We like eye of round best also. It is expensive, but we've been buying it in the cryovac pack. The price per pound is really good that way & I just cut it to the right size & freeze the other ones. I usually get ~3 - but that means hot roast beef sandwich leftovers for a couple days, which DH loves!
Before I got spoiled with the eye roast, I always got either top or bottom round. They tend to have a "slab" of fat on the bottom & are pretty lean throughout the roast itself. They're not as tender as the eye, but are pretty good.
I also used to use a bolar roast when it was cheap, but it is often fattier than those above. More often I'll use the bolar or london broil roasts to cut up for beef cubes, as it's cheaper & less fatty than buying what the store does - but that's another topic.
Oh - I always do my roasts in the crock pot. I got a crock as a wedding gift 26 years ago & have never made a pot roast. I just throw in carrots & potatoes, then sprinkle with Kitchen Bouquet & powdered bouillon as I'm allergic to onions & can't use onion soup mix.