I prefer to reside on the east-side when visiting Berlin as I find it a good base to experience the city. As you have noted, there are plenty of sites and activities to enjoy in that area and you will rarely be far from somewhere to eat, drink, shop or take time out and absorb Berlin’s atmosphere. The west side is also worth visiting as there you will find the zoo, Ku’damm (for shopping and more) and the church which was bomb damaged during WW2 and is a sobering monument to that period.

Importantly, as Alex71 has noted, Berlin has an excellent transport system. That means you can travel from east to west (or anywhere else you choose to visit) with a minimum of fuss. A walk through the Tiergarten, a beautiful, tranquil parkland, is an alternative to public transport which will take you away from the often frenetic tourist areas as you move between east and west Berlin and give you a chance to recharge your tourist battery along the way.

I am not sure which hotels you have sought rates from. However, I believe you will find hotels, representing all accommodation standards, at competing prices at either side of the city. Berlin has a significant amount of hotel space available and IMO is one of better value cities to stay in Germany.

A lot will depend on your particular interests, your budget and the time you have available to stay in Berlin. As you haven’t indicated same in your OP, it is difficult to offer further advice.