The food is amazing and the atmosphere makes you feel like you're not in Boston anymore. Not the prettiest place, but gets tons of props for being intimate.
While it gets a little loud in there, I still think Giacomo's can be a good spot for a romantic dinner. Savvy Budget? I think it fits that -- entrees are 12-15 and you can keep it under 50 if you don't order wine. I prefer the South End location (since they take reservations). Split the tiramisu at the end.
The budget is up to you -- it is definitely possible to do tapas at Dali for cheap, but it depends on how much alcohol you drink.
As far as cozy and romantic are concerned, this is your spot. Great decor inside and of course the most delicious tapas in Boston. Some of the tables are better than others so if you're really trying to impress see if you can finagle your way to one of the more romantic corner tables.
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