You have picked a wonderful time to visit ... it's sunny, days are long, everything's open, nothing is crowded, AND hotel rates are lower than June. The water is swimmable (in Naxos, probably not off those cold rocks below Oia!! ). Exactly the time of year I've enjoyed greece during 11 of my 12 trips. However, "old hands" cannot help you with your budget question, based only on the vague information given. You have 15 nights/days, and 4 people. Here is what you leave us wondering:
• is $1,000 "spending" supposed to cover 4 people or just one?
• is it meant to cover just hotel per person/per pair ?
• Is it meant to cover Hotels AND Meals and other daily expenses? For one? (for 15 days that would be $60 per day)
• What is the cost of Costas Regas per night per double?
.... you see what I mean?? We can't possibly answer, based on information we have.
I can tell you this ... I've had a number of newcomers come with me on 9 of my "budgeteering" trips to Greece, as "travel pals" (I'm not a tour leader, I'm a retired Journalist). I've told them that, if 2 share a room, a person with me can cover ALL basic costs on about €70 a day -- including room w balcony & view, meals, entry fees, local transport (ferries, shared occasional car rental, taxis), even a sunset glass of wine. Of course, we don't splurge on hotels like Costas Regas -- (I know a budget Gem right near the caldera rim that's $45 for a balcony double w breakfast, free transfers, AND use of a pool). So --- if you want to do it on $60 per day (€56), you'd better cut back your Santorini stay to 4 nights, AND do Athens either at the beginning or the end not both. THose are the 2 most expensive places for lodgings. If you cannot do Athens only at the end, at least just come in the night before and stay at a budget place like Hotel Peris 10 mins from airport. NOTE: if you've booked Costas Rigas correctly (NOT the no-refund/ advance deposit way), you have the right to cancellation or stay-shortening without penalty, up to 2 weeks beforehand.
If you cut short your 2 higher-priced destinations, you're left with about 3 extra days, an ideal time to Experience Antiparos... and it's right on the way back to the Mainland! A 1-hr ferry to PAROS, then take a little bus 10 minutes s. of that port town of Parikia and hop a 5-minute mini-ferry across to ANTIPAROS -- to a gem of an islands most Americans never know about (because it's not on those big travel posters). Staying right in the cute tiny port area, you can walk on flagstoned trails all over, and to several splendid beaches. The BONUS? If you want to do more sightseeing, just hop that mini-ferry back to PARIKIA and spend a day there. When it's time to return to Mainland, by ferry it's an hour shorter -- or you could get a bargain Aegean plane ticket if you check website for "special offers."
Lots of options -- but we can only help you with budget tips if you're specific & detailed about what $1,000 is meant to cover.
As for Santorini dinners out, if you stay in Oia and dine there, you'll pay for the location. However, there are plenty of other places to dine -- I like the rooftop of STANI in Fira (reserve a table ahead) for superb sunset view, AND hearty fare, including wine for about €16-17 per person. In Naxos, you have to try hard ANYwhere to bust €15 including a couple glasses of house red. As for lunches, my gang in Greece usually is hiking down a lane or sitting on some ruins looking at the sea, so we picnic.