My boyfriend and I only see each other on weekends but usually it involves a lot of walking. We walked 8.1 miles on Saturday - from my house to the seafront and then along the promenade to the next pier and back, and then back to my house! It wasn't the nicest of days but it's a great way to explore the area around you and chat and etc. There was a powerboat race on as well so that was pretty cool to watch for a bit.
Next weekend we are going to a monkey sanctuary. It is a huge park (like a zoo but with only monkeys) with mostly outdoor attractions. Could you go to the zoo or something one day or evening and wander around checking out the animals? I know not everyone likes zoos so it may not be for you but we're quite looking forward to seeing the monkeys next week! They've all been rescued and brought back to health rather than being plucked from the wild.
My boyfriend's not into it, but I have horses at home and love horseback riding so when he came home with me for Christmas we went riding. Sadly my stepsister's horse can't be ridden anymore so we just took turns on my horse but he'd never been on one before so he got to try something new and I got to share my passion with him and teach him how to ride. Are there places near you that would offer one-hour rides in the late afternoon or even a nice twilight ride for you both?
Most of our weekends involve walking somewhere and you've already decided to go hiking so that's about the end of my suggestions.
I'm going to keep an eye on this thread though, as I'm sure you'll get plenty of others!