Firostephani is a VERY good choice on Santorini, because it's on the Northern edge of Fira town, very walkable in 10-15 minutes to all the attractions of Fira, yet away from the hubbub. It has MANY hotels facing the Caldera, but not nearly as pricey as "view hotels" in Oia. And on the inland side of these rim hotels, it's only steps to the BUS STOP on the main N-S road, to catch local bus to Oia, runs every 30 minutes or so. (TIP: catch earliest possible bus, 8 or 8:30, and you'll have time to enjoy OIA & take photos before the invading HORDES of Cruisers arrive about 10 am). Also, you can enjoy sunset views from FIrostephani hotels & restaurants without the insane crush of OIA (even in Sept).
To see what's available, you can use booking.com Firostephani ... you probably can't see what's available next Sept (too far in advance), but put in "dummy dates" like June 1- 3, and you'll probably get similar prices & more hotels will show. Don't just scroll down list; click on "map view" and all the hotels that Booking has will show up on a Google map as blue balloons & when you click one, it's price for 2 nights will pop up. That way you can see which hotels are actually ON the caldera --- sometimes hotels "fudge" the location - and say "sea view" which doesn't mean Caldera, it means view to East. Don't look at hotels that are much farther East than the central road, because the terrain slants steeply down. When u see a number of hotels that appeal, (I usually look for ones that have a 7.8 Booking review rating or better) contact them/ Even if booking.com says "fully booked!" that doesn't matter, your dates are not June. Find their direct e-mail and write asking for prices for your actual 2019 dates. NOTE: For hotels that appeal, you might check other traveler ratings on Trip Advisor, because it has that neat feature "ROOM TIPS" click on that & you'l see what other guests advise ("avoid rooms facing pool" "Ask for rooms away from road" "Room 23 is the best!" etc).