This article ran in the Times back in November and has some fun ideas. I'm a fan of Murray's. I secured my breakfast from them yesterday from the outpost in Grand Central. They don't have hot sandwiches at that one, but some bresaola, runny brie, crackers, and grapes worked just fine. Bonus for the market at GCT - it's usually pretty empty in the mornings. As the day wears on it's a madhouse.
http://www.nytimes.com/interactive/2015/11/04/travel/new-york-city-budget-travel.html
Summer streets can be a fun activity.
http://www.nyc.gov/html/dot/summerstreets/html/route/route.shtml
Also, depending when you're here in August there are lots of free or super cheap activities - outdoor movies, music festivals (Celebrate Brooklyn, Salsafest, Lincoln Center out of Doors), culture walks, etc. Also free - Thursday afternoons are the Broadway Show League softball games in Central Park, usually on Heckscher ballfields. You can take in some slow-pitch softball played by cast and crew of shows throughout the city, have a hot dog, ride the merry-go-round, and if it's blisteringly hot, you can pack a swim suit and walk through the water playground at the base of the fields. It'll cool you down and, as long as you don't make a fool of yourself, nobody will give you any trouble about not having a kid along.
In addition to seeing a Broadway show, think about trying some of NYC's immersive theater scene. Sleep No More is an interactive room-by-room reimagining of Macbeth. Fuerza Bruta (bonus of getting you to the Union Square/Gramercy Park Area) is ridiculously fun (warning, you stand for an hour and it's ok). Be prepared to get wet, but you'll dry off plenty quickly in August and Union Square has a charming night time scene indoors and out. Also, if you've never seen the Blue Men, Blue Man Group is a great option.
For a worthwhile splurge, consider The Campbell Apartment in Grand Central. It's a beautiful 20's style affair and the former office and salon of John W. Campbell. Drinks are pricey, but worth it for one or two for the experience. Either one would make for a great beginning or nightcap to a special date night. This place doesn't allow jeans to t-shirts.
OK. I'll pipe down now.
Probably.