Places to stay in Edinburgh

Premier Inn has a location on Princes Street that I found convenient. I don't remember noise issues, but you can read through a bunch of reviews on booking.com to see whether other guests agree with me.

Premier Inns are business hotels without local character, but all that I've stayed in have been clean and well-run. I've never eaten breakfast in any of them; you don't have to pay for breakfast if you don't want it. You can check out all the Edinburgh Premier Inns on the corporate website, premierinn.com.

The pricing model Premier Inn seems to use is that good deals are available if you book early, then rates tend to creep up. You might consider booking a fully-refundable room for your May dates while you look around to see whether you can find something you like better or at a lower rate. Do be careful with the booking; the last time I checked, there were three different cancellation policies to choose from.

I will say that one reason I like Premier Inns (when I have a roommate to split the cost with me) is that nearly all are air conditioned. I'm usually in England in August or September, and you just never know when you'll be grateful for that feature. True budget hotels often don't have a/c. However, in your situation (traveling to Scotland in May), I don't see that the a/c provides any value, so you may certainly be able to find a less expensive hotel that you'll be happy with--maybe even one with a bit of local character.

Yes, I have noted that many folks like Premier Inn. I'm just not sure if we would be disappointed to be in Scotland for the first time and have our first nights' stay in a lodging without local character. We have so looked forward to coming. Still, I appreciate the suggestion. I need to be open to what is truly do-able for us. My thanks.

Having to get dressed and ready for breakfast is a big reason why we have often gotten apartments, rather than B&B’s, and hotels are usually our last choice, if we’re staying for more than just a night or two. We had an outstanding (and quiet) place in 2013 for a week, right on the Royal Mile, convenient bus stop immediately across the street. It was on the southern third of the Royal Mile, closer to Holyrood than the Castle.

We’d planned another trip for 2020, but Covid has delayed that. The apartment was still being rented, but it was already booked when we were looking to make a reservation. But we found another apartment, directly across the street. Next trip, we’ll plan to stay at one place, or the other - perfect location! Apartments on Vrbo, or perhaps Airbnb, might be worth investigating.

You probably already know that Edinburgh can be quite hilly in parts.
However, the bus system is really great, and for 4.50 Pounds a day (lasts 24 hours), you can hop on and off all the local buses at will.
https://www.lothianbuses.com/tickets/
All the information is on this website.

Thank you for the bus information. It will be useful!

Benedict:
There is an app for the lothian buses too, which tells you next bus, times, routes, etc.

Wonderful, thank you. This forum is so kind.

Premier Inn York Street is literally at the end of the tram from the airport. Exit the airport, climb on the tram, ride it to the end and you are at your hotel with about 100 feet of walking at the end. Some rooms have a lovely view over the harbor. Only a few blocks to the train station and you can ride the tram if you like.

You will find your character out and about in Edinburgh.

I have stayed several times at the Inverlieth Hotel. I think it's lovely. It is at the bottom of the hill--north from Princes St. I love a Scottish Breakfast and that's why I prefer a hotel or B&B. This is a small hotel which I like. It does have a very small resident's bar so you can have a whisky back at the hotel at the end of the day. It is family run. I've usually caught a taxi from Waverley Train station. I would take the bus up hill in the morning after breakfast and walk back down after my day of touring. There were some local restaurants or I could get back up to Newtown in 10-15 minutes. BTW breakfasts are rarely at the crack of dawn in Scottish hotels. They may not may not start until 7 AM.

Thank you all for your true and capable help. We just booked with the Royal Scot Club, as the Inverleith and other venues in our price range was showing no availability for our dates.

That sounds like a lovely place to stay!
You can just walk a few feet along to Dundas St. to get the bus up to the centre of town to see the oldest historical parts.
Be sure to keep walking too, along to where your street turns into Heriot Row.
Some beautiful town houses along there.

Arriving in May means you will have more choice with cheaper prices. Here are my comments. I've been to Edinburgh several times. I'm traveling to Europe this summer. I have one night in Edinburgh June 19 and a couple of nights in Edinburgh in August, attending the Military Tattoo. I have booked hotels in the Haymarket district of Edinburgh when I am arriving and departing from the airport. These hotels/guest houses are generally quite a bit cheaper than other hotels, but they are not 4 stars. The tram to and from the airport is convenient and cheap with stops near Haymarket and the airport. There are discount tickets on the tram depending upon your needs.