You understand you said 8 days of travel originating in Kansas City? Meaning that after a day and a half to get some place and a day to get home you have 5.5 days of vacation. Your list is pretty spread out, especially since cost is a motivator. You could easily spend all 5.5 days in one location and two fairly adjacent locations is probably the limit.
So, Istanbul and the Black Sea coast towns of Bulgaria. Best done with a guide/driver from Istanbul to Bulgaria on your time schedule. Open jaw ticket into Istanbul and out of Varna or Burgas. Not cheap
Istanbul to Budapest by air for about USD300 a ticket. Open jaw ticket into Istanbul and out of Budapest maybe USD1000 to USD1400.
Budapest to Vienna by train. Very common trips. USD1000 to USD1300 Open jaw airline ticket into Budapest and out of Vienna. Budapest is fairly cheap, but Vienna isn’t.
Or Stay in Hungary: The air fare will be somewhat cheaper as it will be a Round Trip to Budapest as opposed to an Open Jaw ticket. You can rent an apartment in Budapest for USD50 and up with the average in a really good location being something like USD80 a night. Dining out costs are a little cheaper than Kansas City, but the food is outrageously good. Any entrance fees you run into will be in the neighborhood of about USD5. Wine, beer and the pubs are good and inexpensive. The road trip I suggested below will run you about USD60 for two tickets. Hotels in the three towns can be had for USD80 a night or less.
Friday
Leave
Saturday
Arrive Budapest mid to late afternoon (with jetlag….. or not)
http://www.ispot.tv/ad/7wvw/viking-river-cruises-see-things-differently- (majority filmed in Budapest)
Sunday
Budapest Antique shops and flea markets
http://lostandfoundinbudapest.wordpress.com/2013/05/13/what-to-do-on-a-sunday-morning-flea-markets-in-budapest/
http://visitbudapest.travel/local-secrets/falk-miksa-street/
Monday
Budapest
See my itinerary ideas in the Hungary part of the Forum
Tuesday
OPTION: Morning Train to Pecs (about 3 hours) A fantastic little town in the south complete with wonderful Pedestrian zones, cathedrals and ancient mosques.
https://www.youtube.com/watch?v=g5FxsHmUdNs
OPTION: Morning Train to Eger (about 2 hous). This is a wine town with cellars and vineyards, a fortress and wonderful pedestrian zones surrounded by romantic architecture.
http://visitbudapest.travel/activities/hungary-countryside/eger/
OPTION: Morning Train to Gyor for the old town center and the Archabbey at Pannonhalma and the winery.
https://www.youtube.com/watch?v=5MArgjzdSUs
http://bences.hu/lang/en/
Wednesday
Late afternoon Train back to Budapest
Thursday
Budapest, parks historic old bath houses, the Buda hills, wine on the embankment. Do a lot or do absolutely nothing and love it.
Friday
Budapest to Kansas