Wow - this is a huge question!
First quick note: apparently the whole “super host” thing is a bit of a nothingburger. I was researching that a couple of weeks ago and would encourage you to check it out.
Before we were able to find a permanent rental in London, we used AirBNB for a number of rentals over quite a few months.
If you want somewhere bustling and close to pubs, shops, and amenities, look in central London or just beyond. This will cover many if not most of the biggest/most important sites and tourist spots. “Central London” includes a LOT of neighborhoods, and not everyone will agree on what those are.
For reference: “The Mayor of London's office defines it in terms of the "Central Activities Zone", comprising the City of London, most of Westminster and the inner parts of Camden, Islington, Hackney, Tower Hamlets, Southwark, Lambeth and Kensington and Chelsea.”
Because AirBNB does not disclose exact location until after you have booked, this can be challenging - but if you use the map that AirBNB provides and compare it to your phone’s Google map, you should be able to get a good handle on where the rental unit is.
A good tactic is to identify places/areas/attractions on your “must see” list and pin them on a map. Then look at AirBNB and zero in on rentals near those desired locations, then focus in on units in your price range.
That said, if you are only going to be in London for a week, do you actually need an AirBNB? The advantage of an AirBNB is mostly the “self catering” and “onsite laundry” aspect of things, and if you are just in town for a week, that might not matter as much. The convenience of a hotel is not to be sniffed at. In an AirBNB you will likely be cleaning up after yourself every day, doing laundry and dishes and whatnot, and maybe wasting a few hours that you could be spending being a tourist and having fun.
Before we actually moved here we loved our weeklong stay at Club Quarters Lincoln’s Inn Field, which is near High Holborn and Covent Garden. We had a room with some cooking facilities and lots of connectivity (I was working remotely at the time) and we were in an absolutely awesome central neighborhood. Having the 24/7 concierge and front desk, plus a kitchenette, was perfection. (Please carefully check and call each hotel to make sure you are getting exactly what you are bargaining for, BTW.)
Hooe this was at least minimally helpful! :-)