What type of room do you want, what day of the week are you going and how much notice are you able to give?
The answers to these questions will determine the sort of price you'll be expected to pay. Don't choose a hotel for a restaurant: most hotel food is overpriced and can be beaten by almost anywhere else! I'd always aim to stay in a hotel where I wish to wake up in the morning. I find that's more important that being near to my evening destination. However, Covent Garden is ideal as it's pretty close to the theatres and a great place the following morning for a leisurely breakfast or brunch. It's good for shopping and just mooching around too. Travel in London is so easy that staying too near to Theatres or Train Stations is unnecessary and can also be very noisy, even by city standards.
I've stayed at the Travelodge in Covent Garden a few times - the rooms are good and clean but as a cheaper hotel there is a lot of turnaround all night and unless you are at the end of a corridor or on the top floor the banging doors can be a nuisance for a light sleeper. You can ask for a room with less passing traffic though...
I've tried a few of the hotels in the Seven Dials area too (still Covent Garden) - some are very expensive unless you are on a company budget, but it's a good spot to be if you can get a late room deal.
If you are happy to be a bit further out several people I know have recommended
Qbic Hotel, between Aldgate and Whitechapel (east of the theatre area). App 3 miles from the theatre and 4 ish back to Euston in the morning. My husband has stayed here a few times and loves it - it's classed as a budget hotel but it's fun and funky and more interesting than most so called budget places. Book early and you can get a room for well under £100 which isn't easy. It's cheaper than the Covent Garden Travelodge but just remember to factor in your transport costs - particularly if you are thinking of getting a cab after the theatre...
When you find a hotel you like the look of, do google reviews. Although you might get some extreme reactions at either end of the scale, you'll probably notice some themes developing somewhere in the middle ground which should give you a pretty accurate guide as to what to expect. It's also only one night - it doesn't have to be perfect! Good luck with your decision making