法兰克福机场住三晚 you can consider Hyatt Place FRA

It is one stop from S8 or S9 S-Bahn.  Whole trip is under cover, once you get off at Gateway Gardens station, Hyatt Place is the first hotel.

Transfer UR pts to Hyatt at 1 to 1, this Hyatt Place is still Category 1, 5000 to 6500 pts a night.  I believe it does not go up on the March 28 adjustment.  (Hyatt Place AMS goes from Cat 1 to Cat 2).  Cash rate is 150 euro or up.  The most valuable transfer of UR pt is to Hyatt and Air Canada's Aeroplan, followed by United's Mileage Plus. 

I gather you are Hyatt's World of Hyatt member?  They have free breakfast for the members but charge $ for nonmembers.  I believe this is a policy Hyatt put in place a year before Covid.

I just booked one night for our May return flights AMS-FRA-EWR overnight layover at this hotel.

In London it depends on how many days and what you want to do or just passing by - Renaissance LHR is very good, the bus between T5 and city has a stop very close to the hotel on both directions, 1.62 GBP per trip, much cheaper than the Hopper bus and much more frequent schedule.  At T5 the bus depot is immediately outside arrival hall on the ground level.  Easy Peasy to find.

If you are going in town for a few days, I highly recommend IHG's Staybridge at Vauxhall on the South Bank within a 7 min easy walk thru community garden from Vauxhall station (both train and metro)  Vauxhall is the end station of Victoria line.  Easy walk from the embankment to Westminster bridge.

London transportation now can be paid with your contactless credit card on each trip - tap on and tap off, with a daily cap that the system will calculate at 4am the next morning and only charge you the LESS of actual usage or the daily cap on Oyster card.  No more need to buy Oyster card.  You need to use the same card for one person thru out the day in order for it to track properly.  Each persob uses his / her own CC for this purpose.

London China town has some really good eats.  It is very clean these days.