Mike`s right, but just as a hint, my girlfriend loves good food, so for here birthday I took here to
a nice fusion restaurant (mix of French and Japanese) at the top floor of a skyscraper with a view of entire Sendai, and it was very romantic and appreciated and since this is japan it wasn't really that expensive (little more than a regular diner out back in Sweden)
Id stay a way from guidebook restaurants and just ask around among friends instead...
I'm sure what ever you do it will be lovely, as long as the to of u are there