To best top attractions can all be done in 4 days but I would suggest staying longer in order to do some of the little ones as well.
The best tip I can give you for hotels is to not worry too much about getting a hotel in central London. Look at the attractions you want to go to and see what are the nearest tube stations. Then when you are looking for a hotel, look for ones on the same line so that you can still get to them quickly.
London Eye, London Dungeons and Sea Life
Lucky enough, all 3 of these attractions are next to each other, they all stay open late and you can book tickets for all 3 through the same wesbite which will same you lots of money.
London Eye - although you are not on the London Eye for very long, the queue is what is going to take the most time. Even though you have a time slot booked, you could still be in the queue for over an hour. Plus, you will need to go into the ticket office to get your tickets before you can get in the queue. Once you are in your capsule, you will get beautiful views of London and on a clear day you will be able to see for miles.
London Dungeons - book your slot before the day you want to go to make sure you get the slot you want. You are inside for about an hour and a half and it is fun from start to finish. You go through all the gloomy history of London told by live actors, there a little water ride, there's a floor that moves, furniture that moves and so much more. It really is so much fun.
Sea Life - Once again, book your slot but in this one you could be in there for an hour or a few hours because you aren't shuffled around or made to move on, you can take it at your own pace and take in the beautiful creatures that they have.
Once you are done, you can walk across Westminster Bridge to see Big Ben and the Houses of Parlimont. Keep walking and you will see the statue of Sir Winston Churchill, Parliment Square Gardens, St Margaret's Church and Westminster Abbey.
Madame Tussauds - Book your slot to make things easier on yourself when you turn up and make sure that you go in through the correct entrance as there are a few and you need to make sure that you are in the right one. I'd suggest putting your bags and coats in the cloak room but this is outside when you are in the queue, you can't go into it again once you are inside. You will easily be in here for 2-3 hours going round all the different floors and rooms. You can take your time around most of it so you aren't rushed.
ZSL London Zoo - To get to the zoo, you can take a lovely walk through Regents Park. It is not a huge zoo but it has plenty for you to see. Take your time when walking around, there are usually talks about the animals which are really interesting.
Camden - I love Camden, especially the market where you have a fantastic mixture of shops and stalls where you can get clothes, food from all cultures, books, jewellery, musical instruments and so much more.
Head to Piccadilly Circus to see the huge screens and the famous Shaftesbury Memorial Fountain. Walk along to Leicester Square where you will see the Swiss Glockenspiel which is fun to watch when it chimes as little figures come out and bells ring. Either side of it is the Lego Store and M&M World which are both really fun to walk around. The actual square is a lovely garden that you can sit in and there is usually something going on like themed statues or medals hanging from the trees like during the Olympics. If you are lucky, there may also be a film premier happening at the Odeon cinema on the square.
If you are hungry, you are right next to China Town for amazing Chinese food.
Keep walking along until you get to the Hyppodrome and then turn left. Keep walking until you see St Martin-In-The-Fields church and then look to the left of it as that is where the entrance to the crype cafe is. Yes, it is as cool as it sounds, the crypt really is a cafe that you can go into for food and drink. Then when you are done, you can go into a little exhibit of headstones and grave markers. The church is also amazing to go up and look around. We were lucky that during our visit, there was an orchestra playing so we got to sit and listen to the music, it was so beautiful.
When you come out of the church, turn left and walk a few minutes until you come to Trafalgar Square and the National Gallary. Make sure you check out the art work in the square as this does change from time to time. The gallary is free if you want to go in and check out the art, it is huge so give your self a few hours if you want to have a goo dlook around.
Opposite the square is The Mall, which is the road that leads up to Buckingham Palace. It's about a mile walk but you do get to walk along side St James' Park. If you want to see the changing of the guard, make sure you check online to see when it is going to happen as it happens on different days.