Need accomodations for mother/daughter trip!

I would highly suggest that you look at Airbnb for a small flat in London. We stayed at the Omni at Westminster which was not cheap in my opinion. I feel like the tube access is pretty easy from many locations.

It's much more interesting to take bus in London than the underground. The bus system is extremely reliable with short waits. Then you get to see everything as you ride through town.

Get the rome2rio app and check places you want to visit. Transportation for bus and tube options will populate. It’s very easy. Buy an Oyster card as it’s good on busses and the tube within zone 1&2.
I can’t help you with accommodations as mine were well over $125 US.

The good news is that the bus info on the street at bus stops are in English.
I love London! Have a great time.

My daughter and I stayed at the Hotel Simone in London. It is within walking distance of Victoria Station which connects you to everywhere. It's a small hotel, quirky, run by two identical twin brothers who are a lot of fun during breakfast (my daughter slept later than me so when she made her appearance one or the other would say "Good afternoon!"). The rooms are small but the bathrooms modern. It's reasonably priced too. I would stay there again in a minute. Have fun!
Cynthia

My daughter and I have stayed at Premier Inn at Picadilly twice - it was reasonably priced, very centrally located, clean and quite comfortable (and safe). You might want to check their website. They have other hotels throughout the city as well - we've also stayed at the one next to the London Eye.

London Hotel prices vary a lot with the season. What month are you going?

Assuming summer, I checked the Premier Inn which is a reliable and much-recommended chain, with many locations in London. I like the Blackfriars’ location, between Fleet Street and the river in the heart of London:

https://www.premierinn.com/gb/en/hotels/england/greater-london/london/london-blackfriars-fleet-street.html

A twin room there in July would be close to 120 GBP (not $) a night, which is pretty darn good. (For comparison, the Luna Simone for the same nights came to 140 GBP a night).

One thing I like about this location is the Blackfriars station right there, as well as easy access to one of the best bus routes in London, the #15 which runs east-west between Trafalgar Square and the Tower of London, passing near Covent Garden and right by St. Paul’s on the way. The London buses are easy to use once you figure out the bus maps. Here is a simplified map of the main routes, with the tourist sites marked for easy planning:

http://content.tfl.gov.uk/bus-route-maps/key-bus-routes-in-central-london.pdf

Buses are less expensive than the Tube and have the advantage of offering you some sightseeing on the way. They can be very slow at rush hour, but the Tube is extremely crowded at that time (we gave up trying to get on one at Westminster around 5 pm one day and walked home instead). The best plan is just to avoid travel across town at rush hour; plan a shorter transfer and walk.

There are other good Premier Inn locations as well. County Hall and Waterloo are also convenient locations, as is Holborn. They all by price, with the most central ones usually costing more. But they all offer twin bed rooms as an option.

What annemargaret said.

I used my Oyster card for the Tube only once, to go from where I was staying in Holborn to Heathrow.

The rest of the time I used it for the buses to go everywhere I went that I couldn't walk to during the week I was there. I wasn't in a rush and I know I saw a lot more than I would have using the Underground.

Cherry Court Hotel, 5 minutes from Victoria Station.

We used our Oyster cards for the Tube and buses several times a day, easy and efficient. Easy to use machine in tube stations to add money to cards.

Here’s another vote for the Cherry Court in Victoria. Very small rooms, but great location close to train, bus and tube. Very good prices, you should be able to get a room at your price point. Have stayed there on 5 different occasions. Have a great trip!

We’ve stayed at the Celtic Hotel in Bloomsbury - quirky older hotel but we love it / price can not be beat for central great location , room rate includes an excellent cooked to order full breakfast ( not just cheese and bread etc , eggs porridge bacon the works )
Owned and family run !

I booked Premier Westminster St James park for April. 60 GBP per night. Just a single & room looks small. I think that includes 5 GBP breakfast. I won't expect much for that price but maybe something to throw in my pocket. Looks about a block from a tube station and walkable to lots of stuff. Frankly I could not believe it's so cheap. I even did some arbitrage and stayed an extra night there. The following day i start a RS tour in Paris. The Eurostar better be on time!

You could try a chain like Traveloge UK they have many properties in
London. Your budget however is very low, would you consider a hostel?

Thanks for all the replies! I will be checking out all the suggestions! We do plan to use the bus as well, we are just more comfortable with the subway as we have never used the public bus systems. Our trip is in May. Hopefully its not too hot!