Vauxhall area in London

It's fine. I stayed in that area once.

You're close to the Vauxhall tube station which is on the Victoria line. Only a couple of stops to Victoria Station, three to Green Park. You can get most places fairly easily from there.

Did you get an exact address so you could Google it?

Can I ask what the budget is? The 3 neighborhoods you’ve mentioned are pricey.

Vauxhall is okay but did you check neighborhoods like Holborn or Pimlico or Earl’s Court?

I think it's probably quite good value for money in terms of location. Vauxhall / Kennington / Stockwell area is what I think of as a bit of a hinterland in Lambeth that side of the river. Sort of in between central London and south London.

The Victoria Line tube station at Vauxhall makes all the difference. The Victoria Line is a fast line up into the west end. Vauxhall station and its surrounds is one of those that may attract a few waifs and strays, but it's not what I would think of as dangerous. One stop past Green Park is Oxford Circus which puts you right in the middle of the lights in Regent Street and Oxford Street at Christmas.

As far as entertainments in Vauxhall, it's most well known for its gay pub and club scene. If you're round by the park it may be a bit quieter. There's several clubs in the arches by the station and the main drag after the bridge. My only experience is going to a pub down there a few times with colleagues after a late finish at work, as it's somewhere you can get a drink well past regular closing times if you know where to look. I'm not really familiar with eats down there so I Googled and found this enlightening Time Out article.

https://www.timeout.com/london/restaurants/vauxhall-restaurants

It's a short walk across Vauxhall Bridge to Tate Britain, if you're interested in seeing that. There's Thames Clipper Uber Boat piers at St George Wharf on the Lambeth (Vauxhall) side and Millbank, in front of Tate Britain. Buses from all over pass through Vauxhall bus station.

Can I ask what the budget is?

It's a moving target, but £300-400/ night is what our preliminary search is. In Soho/Mayfair the best I'm finding so far to sleep 5 adults is £500+ on our dates. I'm wondering now if we'll spend a week in that area and move on because Kew Gardens and Windsor are on our potential visit list. My mother-in-law has a cousin in Richmond so we may head down there. We had Richmond on our list for a visit for another time in better weather.

If you are planning to spend time west of London then why not look for a place in the west of London.

I'm usually in Earls Court. 15-20 minutes to Covent Garden by tube. Less than 20 minutes to Westminster.

You should be able to get a Premier Inn at Hammersmith or Shepherd's Bush for less than £100 a night, so £300 for three rooms to give each other space. Breakfast is extra, but there are places nearby to eat and drink.
Only 15-20 minutes into central London.

Thanks for the tips. I have noted a place in Earl's Court and another in Camden. I was hoping to find something where we could walk out the door right into the Christmas scene but that's not likely. We're trying to stay away from hotels while we have the in-laws with us. We all live in different cities and we'd rather have a home or apartment to maximize togetherness in the evening. We all stayed together in a home in Florida last March and it was ideal.

If you decide on a place in Earls Court, run the address by me either on this post or PM. I know the area like the back of my hand.

If you want to be near the Christmas scene, have a look at the South Bank/Waterloo/London Bridge area.
There is a Christmas market n the Suth Bank and you will be near Borough Market.
There are several Travelodge/Premier Inn etc in the area, and although I haven't checked lately, Airbnbs.

Did you check out the Club Quarters hotels?

Last November I stayed in the one across from Lincoln Inn Fields and enjoyed it.

Block and half stroll to Holborn Underground station.

Nice Christmas lights along High Holborn.