More than 10kms (6-7 miles). While it may seem not that far, the traffic sucks and it could take anywhere from 30 minutes to 1 hour for you to get to the Old Town.

Hyatt only have that HR in Hanoi.

Hilton is right next door to the Opera House and a HGI somewhere quite near.

Marriott has a JW (it's not really close to the HR but about the same distance to Old Town, may take less time to travel via the highway) and 1-2 Sheraton on the West Lake (still not very close to Old Town, walking is not recommended but its' a much shorter taxi ride).

IHG has 2 InterContinental (1 on the West Lake, 1 near the JW) and 1-2 Crowne Plaza (the HR itself was a Crowne Plaza).

Your best bet would be Accor with the Sofitel Legend and MGallery right in the city center and a Pullman at a manageable distance.

Other options include Melia, a gold-plated Dolce by Wyndham if you want something bling, or the marvelous Capella with an eye-watering price to match.

But to be honest, I would go to any local boutique hotel that look nice and has good reviews. They would be much cheaper, with free breakfast, some might even have a gym and a small swimming pool (which is the only clear advantage of large chain hotels). Restaurants, spas, and laundry are galore nearby.