I went to boarding school in Newport. Haven't been in either hotel recently, but stayed in both a few years ago.

The Hyatt (used to be a Doubletree) is on its own island, very near to the Marriott. There is a short bridge connecting it to the mainland, which is used for fishing by locals. The bridge drops you off right behind the Marriott/public bus station. The Hyatt had better decor than the Marriott, IMHO, and a fantastic Sunday brunch.

The MArriott is better located because you can walk from the hotel down Thames Street to the various wharves, and even to Bellevue Avenue (if you are adventurous). The rooms are situated around a central atrium that is full of white marble. I cannot remember for certain, but am pretty sure that there are no really great views from the Marriott. The Hyatt would have better views all around. The rooms at both hotels are about the same - tiny.

For elegance, I would try Vanderbilt Hall or the Castle Hill Inn.

If you're looking for food recs, try the Brick Alley Pub on Thames Street, Christie's or Scales and Shells for seafood/lobster, and the Black Pearl for formal.