We stayed at the Travelodge by Waverly. It was a very short walk from the train station. We dropped off our rental at the train station, mid-day, and walked to the hotel easily with our rolling carry-ons, very well-lit streets and doormen at a number of other hotels on the station-hotel route. "We" were my husband, our 15 year old son and me. I would have felt perfectly safe had I had to walk to the hotel, by myself, at midnight.
The train station is very well signed, it is easy to find your train.
The Travelodge was perfect. Clean, comfortable beds, quiet and a great location. No restaurant, but that is not a problem (see below). The staff were very helpful.
There's easy access to the Botanic Garden bus (down the road, by the Scott monument, a walk of about 10 minutes max). The hotel will tell you which bus (and, the bus drivers will, as well). You'll need exact change for the bus. The gardens are lovely!
Lots of restaurants nearby (recommend the "Slug & Lettuce" in the OMNI Centre, a sort-of restaurant mall and cinema, down Leith Street Good food and not expensive! And, right across from S&L is a nice little place that is open for breakfast, inexpensive, not crowded, fast and tasty). Make sure to get a photo under the giraffe outside! We ate a great little Italian restaurant (Bella Italia, located on 55 North Bridge) and had heavenly pastries from Patisserie Valerie, also located on North Bridge.
From the hotel, it is easy walking to all the museums (National Museum of Scotland, Scottish National Gallery, Holyrood House), Edinburgh Castle and all other sights (we only used the bus to go to the zoo and the gardens). If you like chocolate, go down corner of Leith & Waterloo Place, across the street to the St. James Mall and visit the Thorntons store. Yummy chocolates!!!
Make sure, if you get a chance, to come out of the hotel, turn immediately left on Waterloo Place, walk a distance of about 2-3 blocks and there will be an entrance, on the left side, to the park (Calton Hill, Nelson Monument, National Monument) located above the hotel The 360 views are spectacular of the entire area. I wouldn't go up there at night, alone, but would feel perfectly safe during the day (there were a lot of people there when we visited as the weather was incredibly perfect!).
We went on "The City Of the Dead" tour. Lots of fun and very interesting. If you are at all claustrophobic or get disoriented in total darkness, make sure you bring a flashlight (bring one anyway, you WILL want to have it!!!). I was nervous about this aspect of the tour and kept a steady eye on someone's Iphone light whenever our tour guide brought us into areas totally devoid of light (I did it, but was glad to get back outside). Also, DO wear a hat and a light jacket that you won't mind getting a more than a bit of dirty water drippings. It is a damp, drippy tour, and I wished I'd brought a hat for sure (the vault drippings were not what anyone would want in their hair...)! Sturdy shoes are a must for this. The whole tour takes a quite a bit of walking (steep streets) and the floors in the actual vaults are uneven, slippery and wet (stay close to another woman and offer a steadying arm to each other!). Our tour ended at Greyfriars Kirk. But, the kirk yard was closing after our tour, so we didn't get a chance to look around the entire cemetery, as I'd hoped.
If we go back to Edinburgh, we would certainly stay at the Travelodge Waverly again!