I’ve got a really good tan and rested very well.- I'd either reverse the prder os these or change the first verb to the past tense.
with a lot of settings, a remote control- this bit could be deleted, as I haven't seen a high-tech TV without either of these for many years. That would give you a few more words.
on a new TV rather than a new bicycle- again, as they gave you the information about the choice, you don't need to say the rejected choice
Getting rid of unnecessary information would free you up to add some more of your own writing, which would enable you to show your command of English off more. It's a good letter and does the task.