Which area to stay in London?

You have already hit upon a good location, good hotel, with reasonable prices for London. Premier Inn Southwark is on the south bank of the River Thames, easy walking distance to, of course, Tate Modern, but also the Globe Theatre, the London Eye, and across the bridge to the west, Westminster. I think this location is perfect for a first time sightseer.

Stay there! Southwark is fabulous!

Never stayed at this hotel but the location is very hip and trendy! Lots of great restaurants and shops over there. The Tate Modern is an amazing gallery, the Eye is right there is you want to ride it, walk across the Millenium Bridge to St. Pauls and you're in the heart of the old city.

I'm a bit more dubious. It's within easy walking distance to the attractions around Bankside, but it's not especially conveniently sited when it comes to transportation to other parts of London.

Is The Premier Inn Victoria in a better location?

Philip is right, Premier Inn Southwark isn't blessed with lots of public transport options, although in fact the Premier Inn Victoria is only about a tenth of a mile closer to Victoria Underground station than Southwark is to London Bridge (the closest station in each case). Say 6 minutes walk rather than 8 minutes. Bus connections are lot better in Victoria.

We used to always stay at Premier Inn at County Hall. One year they hadn't enuf room for all of us so we stayed at Southwark. Loved it and will stay there from now on. It was a couple of blocks to the tube, certainly no worse that Co Hall. The Clink museum is just down the street, there's a Pret a Manger nearby, the Borough Market, the Cathedral and the attached restaurant (to the hotel) used to be a stew house (brothel).

I'd just check a map and see if the place is close enough to a Tube station to keep you happy. For some strange reason, the walk from the Tube to the hotel at the end of the day is always longer than the walk from the hotel to the Tube in the morning. And Southwark is pronounced, more or less, "South-uhk", were "South" is pronounced as in the American "Southern". Accent on the first syllable.

The Victoria Station area is very well situated (Belgravia or Pimlico), and Rick's book has a lot of listings there. I have stayed at Morgan House a couple of times on the back end of solo business trips, and found it to be fine. We also stayed in that area at a Hitlon hotel, think it was Doubletree, this past spring and found it well located as well. We stayed on points though, I would want to pay full fright.

We like Base 2 Stay very close to Earl's Court.

It's pronounced suth-ick

Diana, To answer your question, "Is The Premier Inn Victoria in a better location?" You would be close to Victoria Station. From there, there are two dozen buses leaving, on various routes. London bus routes 2, 11, 16, 24, 36, 38, 44, 52, 73, 82, 148, 170, 185, 211, 436, 507, C1, C2, C10, and night routes N2, N11, N73, N44 and N136. The Premier Inn Southwark area is served by several bus routes, also. The main one I have used when staying in that location is London bus RV-1. Whatever location or hotel you decide upon, get a tube map to study, but also pick up a bus route map. The buses are also a good means of transportation around London. To continue about Premier Inn Victoria, the price I found online was $246. per night; over the budget you originally mentioned. I don't know how much this matters to you. Anywhere near the area of Westminster or Buckingham Palace is going to go up in price. Any hotel near a tube stop, or with good bus service, with a good rating on Trip Advisor, will work. You can get all around town on tube or bus. Check out Premier Inn County Hall location on their website; you may prefer that.

Premier Inn Victoria would be on the Circle and District lines (tube) to go east or west (and beyond). Victoria line to go north/south, for example, up to the British Museum, or Euston Station. This would be a good option for being close to transportation. The Circle Line is the yellow line on your tube map, and is aptly named, because it makes a circle around London linking many of the most popular tourist sights. Yes, Premier Inn Victoria is a better location if you are looking at wanting multiple transportation options. However, Premier Inn Southwark will have adequate transportation, and with less of a hustle bustle feel to the area, and cheaper price on rooms.