My love, my sweet little prince...only you can decide what to do. You love her. That hasn't changed. Would you truly be able to know she was in the city, going on with her life, without being a part of it? She is a mortal, but it would not be the first time a citizen of Asgard fell in love with those from this world.
I'd spare you this pain if I could. But I cannot. I can only offer my support for whatever it is you choose to do.