Four of us are visiting Manhattan for a week in June. We need 5 or 6 dinner recommendations, given various restrictions and parameters. First, though we anticipate one or two dinners where we'll be willing to splurge, our budgets are fairly tight. Secondly, at least one in our party has some medical restrictions, having more to do with physical intolerance issues than anything else. Ingredients need to be fresh, unprocessed, and preferably gluten free. He's able and willing to work around a wider menu, just as long as he can be accommodated. Geographically, we anticipate most of our time will be spent south of 34th Street, or on the Upper East side. No restrictions on meat intake, or cuisine type. Given all of that, what would you suggest?