Just a 15-minute walk from Old Quebec, Hotel Royal William is in a funky neighborhood that has the occasional homeless person here and the bar/restaurant/pub/casse croute over there. In warm weather, around the corner from Royal William is a street closed off with bollards where you can dine al fresco on everything from Italian food to poutine.
The hotel itself is quite good. We didn't use the bar or breakfast amenities, but many visitors did. Our room on the fourth floor was as quiet as can be; we slept soundly in a super-comfortable bed with crisp sheets, comfy pillows and a comforter that was so comforting we think it was the best we'd experienced.
Clean, nicely appointed; the bathroom was immaculate. The shower floor was slippery, so take it easy getting in and out.
Staff was friendly and super patient during a crowded check-in period.
Overall, you could spend more for less value, and you are only a short walk to museums and the touristy places. There's a great library around the corner as well.
We suggested parking right below the bibliotheque on Dorchester for $18 a day.