Heathrow to London Eye

Where exactly is your hotel? There are several tube stations serving the area, so we need to know to advise you well.

I would take the Elizabeth line from Heathrow to Bond Street, then a southbound Jubilee line train to Waterloo. Then walk to the London Eye,

For searches, at the blue title bar at the top, tap the 5 bars in the left corner. Do your search, select travel forums, filter 6 months and newer.

If Piccadilly to District line is an option, changing to District at Hammersmith simply requires crossing the platform, no stairs.

As AmandaR asked, where in the Westminster area. That's a large area.

We’re staying at the Park Plaza. Looks like Waterloo or Westminster stations would be ok.

For searches, at the blue title bar at the top, tap the 5 bars in the
left corner. Do your search, select travel forums, filter 6 months and
newer.

These instructions are probably for a tablet or phone - if you are using a desktop browser, the search area is at the very top of the page, to the right of the RS Europe logo, has a spyglass and the word "search" and after you type in your search terms, the "go!" button appears. As noted, filter results by 6 months or newer for current info.

I suggest getting the CityMapper app for your phone, it will give you point to point directions using all manner of transit and it includes walking instructions. It updates for any delays on specific lines and suggests the most efficient ways to go. You can tap in/out on the tube, just make sure each individual person has their own way to do that (phone pay, credit card, or Oyster card). Many posts on that topic in the forum.

I'd recommend exiting at Waterloo. We stayed there last year (Park Plaza County Hall, across the street from Park Plaza Westminster) and it was very convenient, especially with luggage. The train station is large and it's easy to get funneled out at a weird exit. If you can, follow the signs towards the Sidings mall area, and exit just before you get to Brewdog. Follow the exit, turn left on the sidewalk at the main road (York Road) going past the Premier Inn, and then you'll end up at both Park Plazas.

I'd vote for the Elizabeth Line to Northern, mostly because the Elizabeth Line is so nice! It was quiet, efficient, and cool. Because we were staying near Waterloo and due to our other destinations, we didn't ride it again, so it was nice to ride that first trip in.

Piccadilly Line was closed when we were there, so we switched at Bond St to Bakerloo because we also needed to stop at Picadilly Circus on the way for an errand. Bakerloo was not our favorite, it's louder and older, my husband did not like the squeaky brakes much. Definitely being picky though, it still got us where we were going!

Another veteran route to Waterloo is the red London bus from any of the terminals to Feltham Railway station, level access to the northbound platform, then main line train to Waterloo. As fast as any of the other routes, and covered by TfL fares.
Before any rail lines served Heathrow it was one of the main routes to the airport and is still well used as such by locals.