Hi Mike and Connie,
there are many hotels within central London and can suit any budget, from about £50 per night. being based in London and travelling out from there is probably better than staying outside the City and travelling in! and to be honest it's not much cheaper than in the City. But here are some beautiful old country hotels on the outskirts you might like to stay at. As for travelling, I would suggest a hire car, Although there is a fairly good public transport system, the railway prices are getting steep, and even although our fuel prices are one of the highest in Europe, renting a car and fuelling it would probably give you more freedom and a cheaper option to get out and about. wouldn't recomend it for use in the City itself, as you could walk a mile quicker than you could drive it! I suppose it depends if you enjoy driving? The other budget option is our National Express Coaches (Bus) they are a cheap way to get further a field. As for theatres! well, what ever you like you will find in the Haymarket, Covent Garden, or Shaftsbury Ave, and the ticket prices obviously vary, but about £48 each will get you nice seat for Phantom, I don't know how much of London you have seen, but there are tour buses with commentry operating regularly around the city! and can be a great way to get orientated. All our Museums and Art Galleries are free entry! There are some great markets around too, and the usual warning about them applies! As anywhere, London has it's darker element, and there's certain areas you wouldn't want to visit after dark, and of course we have our fair share of criminal types!
Moving around in the city, It's not that big, so if you enjoy walking, and can read a street map you could try that, or there are the Black Cabs, not too expensive, and can be hailed from the street, be aware of any others unless recommended by Hotel. The Underground (subway) can be daunting, very busy at peak times but a good way to move further about. The services buses are plentiful, but even I can't understand the timetables, and they don't take cash any more, you'll need an Oyster Card and charged with credit (purchased from any shop displaying the sign). Be aware of our Congestion Zone, which will cost £10 per day if you travel in or through it in a car!
As for seeing more of the country, well there are plenty of operators offering a wide variety of tours from one day to one week, so it all depends on what you want to see! Let me know and I'll see what's out there for you. If there is anything in particular you want me to find out please feel free to message me or leave a post on this thread
Kind regards
Kev & Julie