This is the key phrase there:
I might use this class in other projects and not just the asp.net MVC project.
A controller is HTTP-centric. It is only there to handle HTTP requests. If you want to use your model in any other project, i.e. your business logic, you can't have any logic in the controllers. You must be able to take off your model, put it somewhere else, and all your business logic still works.
So, no, don't access your database from your controller. It kills any possible reuse you might ever get.
Do you really want to rewrite all your db/linq requests in all your projects when you can have simple methods that you reuse?
Another thing: your function in option 1 has two responsibilities: it fetches the result from a mapper object and it displays it. That's too many responsibilities. There is an "and" in the list of responsibilities. Your option 2 only has one responsibility: being the link between the model and the view.
