Hi. I stayed at the Premier Inn County Hall as a noobie, and several times since. Make sure you google it that way and include the County Hall location as there are a few Premier Inns in the area. The location offers restaurants; grocery/supermarket in Waterloo station; ATM machines; a great place to walk/stroll in the evening: Southbank Walk. Close to Waterloo underground and train station and Westminster tube station. Easy walk over over the bridge to Westminster and Parliament. Plus, with fairly easy walking, you can visit many sites from this location, including Tower of London, Borough Market, Shakespeare's Globe. In fact, here is a link to something called the Queen's Walk. I never saw this before, but have done the walk :-)!
Westminster tube station is on the Circle, District, and Jubilee lines and Kew is reachable on one of those, I believe. Bus routes stop at the corner going over Westminster Bridge. In the past, the rear of County Hall, where Premier Inn is, has been a pedestrian zone as the London Eye is right on the other side of the building. Having this buffer along with accessible little shops and restaurants is nice.
Don't be overwhelmed. You are not dreaming. This is doable. And this is my favorite location for low stress access to many sites. Another handy website is Transport for London: https://tfl.gov.uk/. See the Plan a Journey feature. You can use County Hall as a location and plug in the sites you wish to see. You can edit types of transportation: tube, bus, train, river, walking, etc. If you don't like escalators, you can note that. Very user friendly.
Also, although you are asking about places to stay and not sightseeing per se, I recommend looking at the London Walks website as their (low cost) walking tours (just show up, not pre-ticketing) provide introductions to many places - many that I would not even have thought to explore on my own.
Have fun. You can do this.