Hotel near Globe Theatre

There are lots of big chain hotels in that area. Using my brother's free hotel points, I recently enjoyed a stay at the Holiday Inn Express London-Southwark. A short walk to the Globe, or bus line RV1 to Covent Garden gets you close to other theaters.

One way to look around is to go to the Google Maps site, type in Globe Theatre London, click the Nearby button on the left side and then Hotels. It will locate a number of places on its map and some will have links. I'm not saying the site is thorough or complete or that quality is evaluated. Consumer be wary. But it is a handy start for further research, especially since you can choose a hotel and then click on functions to see nearby pubs, restaurants and attractions. It maps transportation, too.

In 2015 I got a special rate at the Mondrian London at Sea Containers, an easy walk to the Globe and many other sites on the Southbank. I had a view of the London Eye from my room, illuminated at night. Compared to a really cheap (for London) budget hotel, I figure I got 5 times the room and experience for 2 times the cost!

Premier Inn London Southwark Tate Modern hotel:
http://www.premierinn.com/gb/en/hotels/england/greater-london/london/london-southwark-tate-modern.html?cid=GLBC_LONSOU

The Premier Inn Southwark is probably the closest hotel to the Globe. Be warned, however, that the area is not especially good for public transport to other parts of London.

Another vote for Premier Inn or Mondrian if budget allows, a short walk across the Thames gets you to St. Pauls on the central line... But tubes are limited south of the river.