We've stayed at the Four Points now about a dozen times. For the kind of travel we do, with dogs and 11-year-old in tow, it works better for us than Loews (too precious), LaQuinta (not precious enough!) the Brown Palace (not dog friendly), Doubletree (too far from everything) or the Monaco (too snotty.)
We generally ask for a room with an outside entrance, and generally end up with one poolside, which is a very nice place to sit and eat room service breakfast-- and is very convenient for taking dogs in and out.
They are in the midst of an enormous renovation, so if you don't have patience for that, stay elsewhere. For the longest time they featured a room rate of $59, couldn't beat it at the Motel 6, but alas, those days are gone. Still, you can get a room for less than a hundred bucks, and that is a great thing in Denver.
Sheraton's signature beds are so much more than just comfortable, they are exquisite. Lighting is good, rooms are clean, not much bother from noise. Bath has great Speakman shower and a nice curved shower rod, excellent towels. Door handles are sometimes a little quirky... you move them up to open the door instead of down, but I think they're working on that. Complimentary bottled water, real coffee cups (instead of styrofoam or plastic) and real glass glasses to drink from.
On one occasion when I stayed here, there was no water, no cups and something else was awry. The front desk manager arrived at my door with a handwritten apology and a box of chocolates. I actually didn't need to be mollified, as I wasn't angry about the lapse, but their gesture was charming none the less.
Front desk staff have never been anything less than totally helpful... particularly Sean, James, Momadou, and Lina. Room service has been adequate, food is quite good, but it can take quite a while.... it is a huge hotel-- a bit labyrinthian, but we find our little corner, down by the pool to be quite nice.
If you want to go out, the Sushi Boat next door is great fun, and we always try to hit the New York News Deli down the street for a great breakfast or late night dinner.
We have always found this hotel to be a pleasant and stress-free place to stay while we're in Denver, and recommend it. Just don't ask for our room by the pool!