Yes, the most famous mosques, Topkapi, Ayasofya, Sultanahmet Square, Grand Bazaar and other tourist-friendly places all are on the European side of the Bosphorus.
But if you are in Istanbul for more than three days -- and no one should visit for less than a week to 10 days -- go to the Asian side.
The cost for the ferry is barely more than $1 USD.
The ride is amazing, with views of some of the most important buildings in the world.
Then you arrive in Asia. It feels the same, looks the same -- though a lot more secular than, say, Fatih on the Eastern side.
Üsküdar is very much worth visiting.