Good value London hotel, etc.

There are some good suggestions for budget hotels on this recent thread:
https://community.ricksteves.com/travel-forum/england/budget-hotel-london-similar-to-celtic-would-be-great

Good suggestions on this thread also:
https://community.ricksteves.com/travel-forum/england/kensington-gardens-vs-darlington-hyde-park

Another great deal in London are the YHA hostels, in several different locations all over London. Hostels these days are 100% better than say, 10 years ago when they were not very nice. Check out the hostels. Some have their own cafe serving breakfast, and the rooms are clean and nice.
Oxford St -- http://www.yha.org.uk/hostel/london-oxford-street
Central -- http://www.yha.org.uk/hostel/london-central
St Pauls -- http://www.yha.org.uk/hostel/london-st-pauls
St Pancras -- http://www.yha.org.uk/hostel/london-st-pancras
Earls Court -- http://www.yha.org.uk/hostel/london-earls-court

Best location for your son may be "Central" because it is walking distance to many tourist attractions. It is a very large hostel, so they have more services, such as a cafe and a bar, and walking tours. However, all of these I listed are in good locations for seeing the sights. If your son and friend book a "Family Room", they will have a room all by themselves. Still very inexpensive, and far lower than the cost of a cheap hotel in London.

Under "Availability", select "Private Family Room--Sleeps 2 People" from the pull down menu. Cost will be from £40.00 per night, up to £75, depending upon what night of the week you want to book.

"Hop On & Off a good idea?" Yes. Just be sure they take full advantage of their ticket. When they first get on the HOHO bus, stay on for two hours, and you will get a complete loop all around London and get a drive-by view of all the landmarks/important sights, with a guide giving narration of what they are seeing and its history. That way, if they don't get to go to everything and go inside, at least they've gotten a quick look from outside. Then for the next 22 hours (your ticket is good for 24 hrs.) they can use the bus for transportation from one sight to another. (But they don't run all night. They should ask what time the buses stop running.) Their ticket is still good the next morning for awhile, provided the 24 hours has not run out since they bought the ticket. All HOHO bus tickets include a boat trip on the River Thames. They don't want to forget that; it's a great way to see the city from the river.

I second YHA if they want to save as much as possible. There's also Thune Hotels and EasyHotels that are other budget options.

That being said, I like the hotels in Rick's book, like the Lime Tree. They are more expensive, but I find it worth it to get the awesome breakfast.

For nightlife, atmosphere and good tour options, YHA is probably a safe bet.

To answer your other question. Kensington is a good area, but expensive. If your son has a copy of the Rick Steves London guide, have him take a look at some of Rick's budget hotels. There are many, many hotels listed, too many to repeat here. Most bookstores and libraries have Rick's books.

We have stayed at the Crowne Plaza Hotel, South Kensington, a few times. It is right across the street from the Gloucester Tube Station. You can also walk a short distance to Kensington Gardens, one of the museum's, etc. It is in a lovely, safe and convenient area. The next time we go there, we are going to book a Club Room. That will entitle us to use the lounge and its benefits. Then we can eat in the lounge any time of day. The Crowne Plaza is part of the IHG Hotel Chain (Holiday Inn, InterContinental, etc.) If you join IHG, it is free. Then you earn points towards other hotel stays. You can get upgraded when you are an IHG member also.

They might appreciate being close to SoHo/Bloomsbury area (Think Tottenham Court Tube Station) It's just off the Piccadilly Line (on the Northern line) - Piccadilly Line is the only one from Heathrow and the most effective way to get into the city.

x2 as Kensington area is spendy. They might look at The St. Giles Hotel. It's a hopping place 24 hours a day and has a 24 hour diner on the ground floor. It's in Bloomsbury/SoHo area

The "Original London Tour" Red Route is a 2 hour "hop on hop off" that shows you everything (crosses the Thames about 5 different times) and is about £30 per person. It's touristy but fun at the same time!

WhateverLA

I suggest searching "Rick Steves Forum London hotels" via Google and read through recent threads on the topic if you haven't already. Your question or some form of it gets asked frequently. There have been a lot of suggestions over the years. Your son may want to consider the Paddington area in his search. Convenient and there are some moderate small hotels in the area.

Just a reminder that Central Line Trains are not stopping at Tottenham Court Rd until mid December. With such a short time in London, be sure to check the Transport for London web site for transit closures to be sure you are close to your transport links.
Pick out what you want to see and look for lodging that puts you convenient to that location.

Forgot to mention - Hop On Hop Off is great on a Sunday. Sign up for emails and you will get discount offers.

I visited London a few years ago when I was 21 and also 22. The second time I stayed with a friend but the first time I stayed in Generator Hostel
It was really lovely and also had a bar and was a good distance from the attractions. I think hostels are more fun for travelers in their twenties anyway because it is really easy to meet people your own age. AND....hostels can be super nice. They aren't all dumps just because they are affordable.