A recipe website that allows users to search for and share their favourite recipes. Users could also leave ratings and reviews for each recipe. 

A travel website that helps users plan their trips by offering recommendations for hotels, flights, and activities. The website could also allow users to share their travel experiences and photos.

A fitness website that offers workout plans, nutrition advice, and other resources to help people reach their fitness goals. The website could also have a social aspect, allowing users to connect with each other and share their progress.

A fashion website that features clothing and accessory recommendations based on the user's style and preferences. The website could also include a virtual try-on feature to help users visualize how an item will look on them.

A personal finance website that offers budgeting tools, investment advice, and other resources to help users manage their money. The website could also have a community aspect, allowing users to ask questions and get advice from financial experts and other users.

These are just a few ideas and many other possibilities for a new website. The key is to identify a need or a problem that your website can solve and then create a solution that meets that need uniquely and innovatively.