Buckingham Palace is an easy stroll from that Premier Inn. Maybe 15 minutes. Parliament Square:
( Parliament, Elizabeth’s Tower with the Big Ben
bell and Westminster Abbey ) is 20 minutes away.
A favorite and lovely pub, the Buckingham, is near by. Windsor Castle pub has been refurbished. Another spot to rest your feet. Or my favorite pub The Two Chairman on Dartmouth @ Queen Anne’s gate. FYI through the years, Queen Anne’s Gate road and buildings, have been used for interior and exterior filming.
If you get out before 10am and wander toward St James Park and the Wellington Barracks you can watch the soldiers march toward the Palace for the Changing of the Guard ceremony. Stand on the corner of Buckingham Gate and Birdcage Walk and you’ll see and hear them.
As far as tube stations: Victoria, St James and Pimlico.
Giraffe, a perfectly fine London restaurant chain, is a 2 minute stroll from your accommodation.
As far as anything else before you go, use Google Maps to see whats close by the Premier Inn locale.
Lastly, a hidden gem is Westminster Cathedral. Gorgeous exterior and interior. Not to mention a world famous choir.