I've stayed at the Staybridge Suites a few times including earlier this month. It's quiet and clean. Free breakfast, evening reception M-W and a free laundry room. They have one bedroom suites with a pull out sofabed in the living room. If you need two rooms that won't be a problem.
Dundee is not that big. Nothing is really more than a 15 minute walk from the hotel. Much of the center is a pedestrian area.
Connected to the Staybridge is a Hotel Indigo. Same management and check in area but different concept. If you don't need the kitchen, the Indigo might be the way to go. (There is also a restaurant on the premises. (Daisy Tasker).