Greece will be tough--any port city will be very busy thru most of Oct. Seriously, take a look at Malta.
Another thought--have you been to Prague? We love Budapest, too (zed req'd). I've only tried Greece once and I got RT in biz but 24 yrs and S2. I don't think there are advisories for IST.
What sort of budget would work for HKG hotel? There are SO many options. I've stayed in a few places there. We have Accor deals there, too--Novotel for sure. We like HKG so much we stayed a total of 9 nts, ending in Chinese NY.
Hasn't Chile dropped the arrival fee for Americans?I've not been but I'm sure a few others have. Should be nice weather.