Zurich may have it all. Picturesque walkways, endless options for restaurants, cute little shops, a river, and a beautiful lake with (of course) the Alps in the background! On a sunny day, you could easily spend all day wandering through the city or lying by the lake after a refreshing swim.
If you are looking for a funky destination that locals enjoy, check out Frau Gerolds Garten. Its location is not central, but it is definitely worth the effort to get to! It's an outdoor eating area, where old storage containers have been turned into shops and food stands. A garden gives this place a park like feel in an otherwise concrete jungle. From there you can hop onto a tram towards the main train station, which from there leads you to the Bahnhofstrasse, a shoppers delight. I would suggest taking one of the side roads towards the old town for a more peaceful and romantic stroll through the city.
It won't take long before you stumble upon the the river, Limmat, that leads to Zurich lake. Stop at Restaurant Schipfe 16 for a relaxing drink on the water. From there, make your way towards the lake for a swim. You can jump into the water practically from anywhere, but I would suggest jumping in at a restaurant called Fischers Fritz. Included is a campsite, so there is a nice grass area to lounge on. For 5 francs you can park there all day and use the restaurant for drinks and food while sun gazing.
From there, make your way further along the lake for about a 20 minute walk to the Rote Fabrik. There you will find a laid back (and more affordable) restaurant called Ziegel Au Lac that opens its doors right onto the lake. A great option if you are looking for vegan/vegetarian options!