I would walk from Euston to the British Museum. It’s a really straightforward route basically just cross the road opposite Euston, walk straight ahead until Great Russell St, turn right.
I would then walk down to the Strand maybe via Covent Garden, but you can just carry straight along the road you came from Euston.
Cross over Waterloo Bridge and admire the view of the Thames.
Then you will be right near the London Eye. Personally I wouldn’t bother, but up to you.
Then you could:
Walk along the South Bank to St Paul’s or the Tower. I would just pick one, as they are expensive, so shame to rush. You get to St Paul’s first. I would allow an hour for a stroll there.
Or you could get a river boat from the pier by the Eye to the Tower in about 15 minutes.
From there, a tube back is quicker if you are short of time. Buses can get stuck in traffic.
From the Tower, tube stop is Tower Hill, Circle Line (yellow) West to Euston Square. Walk to Euston station.
Or from St Paul’s tube station - central line (red, the only one) one stop east to Bank. Then Northern line north to Euston itself. Or to avoid having to change, just walk down to Bank and go from there, it is straight down one road, so easy to find.
The tube might be a bit daunting if you have never been on a train. Just remember if it is crowded, that lots of people will get on and off at both Kings Cross and Euston, so you can follow the crowd, even if it is looking like you won’t possibly be able to squeeze your way out.