Thanks for the responses. I think I'll definitely rule out HEX... the £33 is the current price i could get for 2, 1-way tickets with about a month in advance. Based on playing around w/ travel dates, the price will go up if I were to wait even a few days.

So now looking at Uber or Tube, and it appears I'll be staying close to Charing Cross (haven't booked hotel yet, but likely staying across the river from the Eye), so Tube to Piccadilly and then a 10 minute walk seems reasonable. We'll have very limited luggage so should be doable if we go that route.

Will likely make a decision on arrival based on traffic, Uber cost/wait, and weather.