Da Nang is the way to go. It's very cheap, fun and food is great. Singapore is farther and much more expensive (2-3x) for all things and Manila/Cebu is a further flight. Apply for a Vietnam eVisa (~3 days) and you should be good!
I'm deciding whether to get a Tourist Visa at the embassy or just risk it and go to BKK airport...
The hassle comes from the requirements/docs you need to bring to Embassy. Application Form, Round Trip of Flights, 6 months worth of bank statements, receipt of accomodation for ENTIRE time in Thailand, and photographs. It isn't that difficult TBH but much less work to just buy a plane ticket and show up at the airport.
Those two countries are *must-visits*, wouldn't even compare it, just go. Both places are convenient, amazing food, great people and ton to do. Vietnam is on the same level as far as price (might even be cheaper) but Japan is a bit more expensive.