Northeast corner of Dempster and Harlem, in a small strip mall, there is
Lai Thai. Excellent Thai food for a very reasonable price. They earned four forks in a Tribune Cheap Eats column a couple of years ago.
Heading north on Milwaukee from Dempster: Within the first block and a half, on the west side of the street there is a Phillipino gorcery (sorry don't know the name. They're in a small strip mall and are the only Asian grocery store in that area. Tough to get it wrong) with a cafeteria style counter in back. There's only one sit down table so you'll probably want to get it to go. A nice variety of skewered meats, stews, and noodle dishes.
At Milwaukee and Ballard, northeast corner, you will find
Burrito House. Never been to this particular location but, I
very regularly frequent several of their city outposts and believe them to make the one of the best burritos in town. They serve a style of burrito that
does not include onions or cilantro so, if you want them you'll need to ask. Likewise avocado.
Proceeding north you will find, on the east side of Milwaukee one of the many
Los Camales Tequerias that are found throughout the city and 'burbs. Not my fave for Mexican but from what I understand, very authentic.
Finally, less than a half mile north of Golf, on the west side of the street, is the beloved
Pita Inn. Is there anything I can say about P.I. that hasn't already been said on these boards? If you're continuing west on Dempster after lunch, simply take Greenwood south instead of Milwaukee and you'll wind up significantly further west.
Once you get west of Milwaukee on Dempster, it is little more than Fast Food Lane (the one exception being a NY Bagel & Bialy in the shopping mall across from Lutheran General). By the time you get to anymore real food you'll be all the way in Des Plaines on Miner Street.
Good luck,
Buddy