NOSA: Aww this is cute. You're not going to find a cheap restaurant that's "not common" so you might have to "manage". For this price range, I usually recommend La Taverna. Both of you can split a pizza and get a sangria pitcher without spending over 5k. The pasta might put a squeeze on your budget.
FOLLY: A breakfast date at La Brioche perhaps?
NOSA: Another option Basilico, but you'll have to settle with one of the lower end pastas on their menu.
NOSA: Sailors is absolutely terrible. Have you looked at the water in their waterfront patio? Completely disgusting.
As for weekday hangouts, you can't go wrong with Hard Rock. It's very snapchat friendly.
NOSA: I know you said no "Chinese", but Zhou Jie Hotpot has proper Chinese food that they're appreciate. Otherwise, go with Casper & Gambini's. Safe pick.
FOLLY: Hard Rock is also an option, but make a resrvation for them cause it gets busy.
FOLLY: Affordability is relative, I'm afraid that's just too little information for me to make a recommendation.
NOSA: This is a bit vague. Would be nice if you gave us more to work with. As you haven't, I going to go out on a limb and say Liquid Hub.
NOSA: 1415. You HAVE to do 1415.
FOLLY: There's no live music but the occassion is definitely worth 1415.