Recommend a beef roast, please!
What cut of beef makes a good roast that is not too fatty and not too tough
It depends on what you want, I like a chuck roast for fall apart goodness, cooked until the fat melts, more of a well-done roast, served with gravy and potatoes.
I like a tenderloin for a medium cooked, thin sliced meat, served at room temperature.
A brisket is great, cooked low and slow, but better smoked!
and then, there is prime rib....
Filet mignon would fit not fatty and easy and relatively quick cooking that yields tender, albeit not incredibly flavorful, meat.
But, that's what sauces are for!
Spoon roast, which is a sirloin roast...cooked to a medium rare. I won't say its a lean cut tho. also really good slow cooked on the grill.
a little olive oil, kosher salt, fresh ground pepper and garlic.
It will help if you say more about your serving plan and also, relatively speaking, what counts for you as "not too fatty."
Referring to the responses so far, for example, if you really want a low-fat (for beef) roast, then the Cooks Illustrated recipe for eye of round could be a winner. But that roast actually has so little fat that you cannot produce a gravy from it very well, and also it needs to be served in quite thin slices--like for a roast beef sandwich.
In the other direction, a chuck roast is delicious but definitely fatty and also unctuous from connective tissues that break down into a kind of gelatin (yummy but heavy). It's best as a braise or pot roast, I think.
An awesome (if expensive) is a strip loin roast, or of course a prime rib roast. Here's a Chow thread to get your started:
An advantage of the strip loin is that it's generally boneless and quite uniform; even cooking is therefore easier than with prime rib. But the rib bones on a rib roast are favorites for me, so that's incredible, too. There's a reason these are the most expensive of typical roast cuts.
Personally, I do not think an Eye Round makes a good Roast Beef, as I find it dry and lacking flavor for my tastes, regardless if it's cooked to medium rare and sliced thin. for the same money, there are better options for me to consider and enjoy.
Assuming you are looking for modest priced option, here are my suggestions. You make have to seek out a butcher or speak with the butcher at your local market for a special order for the weight you need for one single roast....or you can roast two smaller ones.
Shoulder/Cross Rib Roast (Fore)
Whole Top Butt Sirloin...*The Poor Man's Roast/Prime Rib*
Knuckle Joint/Bottom Sirloin (Hind)
Top Blade Roast (Flat Iron)....you would need two
I happen to like Chuck Roast for myself, and I have made some really incredibly tender ones in the past,and a few clunkers, but you need to have them 3-4 inches thick and roast them low and slow for best results. Have a look at the following threads to see the results in pictures. The !2 pound 4 inch thick cut I had specially cut when a local supermarket had them on sale for under $2.50/lb....
For the Cross Rib/Shoulder:
Definitely chuck. If you haven't tried it this way, add 2 T steak sauce, 1 pkg. dry onion soup mix and a can of cream of mushroom soup and wrap the whole thing in foil. Don't peek--just cook at 350 for 4 hours (any size) and when you unwrap it, you won't even need a knife to cut it. Have plenty of rolls for sopping!
I like a faux fillet. It does have some fat in it but eat around it, and it is very tender and expensive.
Assuming you want to roast something and not braise (pot roast), a lean and tasty roast is the sirloin roast, Strip roast (NY Strip in roast form) or if you can go with more fat, probably the tastiest is the Rib roast or rib-eye roast.
Chuck for sure but if you're getting it from a butcher shop tell them you want the end of the chuck that is the fattiest. The collagen will melt like butter. 'Low and slow' @ 200F covered until the internal temp is about 135F. Remove and rest and the carryover' will raise the internal temp a bit. Beef doesn't need to be screaming hot when served if the sauce/gravy/garlic mashed Yukon Gold mashed potatoes/fresh carrots are IMO.
The OP never specified whether s/he is talking about roast beef or pot roast but since s/he asked about eye round in a downthread post, I *think* the question refers to roast beef, in which case some of the other responses are on the wrong track for this thread, e.g., mucho gordo's chuck, which creates a great pot roast but uses foil wrapping to create a braising environment rather than the more typically-used Dutch oven.