From East of Central Ave, it's 30-40 minutes to FiDi or Midtown, plus any additional walking or transit once you're in Manhattan. Choose your own adventure of walking, biking, bus, light rail, train.

The buses will take you to PABT in midtown or to JSQ or Hoboken for PATH to Midtown or FiDi, whichever you need. Light rail pro tip: follow the Hudson Bergen Light Rail twitter account, they post live updates on any issues. The official NJT app only has the light rail schedule, no updates. You can buy tickets for bus and light rail on the NJT app, though the conductors almost never check on the light rail. PATH service is pretty good (most of the time) during peak hours but not late at night.

Here's a map of restaurants/cafe/etc that I made, it's very much a work in progress but I count a dozen well/highly regarded cafes/bakeries along Central and Palisade (you can toggle the map layers to see other establishments). And as others have mentioned, Riverview Park is great (farmer's market and all) and Washington and Pershing parks are also nice.

Parts of the Heights are definitely a food desert, though I anticipate that will change sooner rather than later. A lot of the corner stores / bodegas are kinda trash. Supremo and Stop & Shop are okay. There's a quality Shoprite and Trader Joe's in Hoboken, not convenient but not too far either. Whole Foods in Weehawken (further still). Buy a little push cart, I guess. Grocery shopping is easier if you have a car but having a car in the Heights is a pain.