Is Easter the day you will be arriving from the US/Canada on a transatlantic flight? If so, you will probably be sleep-deprived and jetlagged enough that you aren't up to full-scale sightseeing. The usual recommendation for Day 1 is to walk around outside, possibly taking a brief nap (set your alarm!) when you can get into your hotel room.
I enjoyed the three London Walks I took last September. You don't have to arrange them in advance; you just show up and pay £10 per person, so this is something you can make a decision about upon arrival, when you know how you're feeling. Unfortunately, I cannot get the website to display the list of walks scheduled for April 1. I've emailed the company and will post again if I am able to obtain the information for you.
You could also check for a RickSteves audiotour, or use a printed walking tour from your guide book. You really do need a guide book for a large city like London. It's false economy to try to get by without one, because a good guide will save you money in lots of ways, including on public transit.
I think you'll find that most of the sightseeing attractions are open, if you've got the energy to tackle them. (I never do.) The websites of individual museums and sights always show hours of operation; if they will be closed on Easter Sunday, it should be noted.