I'd say this works better if you're already in a relationship, or if the other person likes you REALLY much:
Pull a 'Before Sunrise/Sunset' and go for a walk/exploration around the city together, spontaneously doing anything from randomly catching a bus to anywhere you feel like, randomly trying new restaurants/hangout places, dancing/singing in the park and otherwise being spontaneous, silly, and fun.
Stop at a park together and chat or romantically embrace, go to the beach and play-fight as you try and push the other person into the water in their regular clothes! Physically play and mess around on some stairs or something, lie under the stars, walk anywhere you want to, do anything and everything you want to, together.
Ensure lots of conversation, playful banter, and overall that you're both having a good time.
To make it more interesting, try to see what fun you could have with a very low budget.
This isn't necessarily impossible - where I live the local art gallery/nature museum is gold coin entry, and cheap restaurants do exist if you require a bite to eat.
Otherwise, it can be as expensive or cheap as you want it to be.
Your own city will do just fine, but when on vacation at a holiday getaway, it's even better! 