Lucky Platter is one of those places people seem to love but darn if I can see why. Maybe it wins on a total funky atmosphere thing, and I can accept that, but I've never had a meal that went above B- there.
Probably the best nearby strip for Greek coffeeshop type places-- which is what you tend to have instead of diners in areas built after the 60s or so-- is in Skokie (I think) along Touhy, west of the Edens. Jack's and other places along there all do a pretty decent job with the usual stuff.
In the city, you're not exactly close to, but not insanely far from either, Pauline's at 1754 W. Balmoral, which has a Lucky Platter like ambience and pretty good breakfast-- like LP, perhaps overrated, but in Pauline's case I'd consider the truth and the reputation to be more than distant relations.