First of all, CONGRATS!
In 2009 my bride and I spent three wonderful weeks in Krakow, Budapest and Vienna. All our airfare and hotel in Vienna were "paid" with miles/points.
I would suggest both you and your fiancé signup for the Starwood and either AA or UA personal and business cards. Now you will have to achieve your respective minimum spends in whatever manner you two can do on your own and or through creative tips on FT.
I strongly agree with one of the other posters who suggested you concentrate on just one large city if you only have basically one week. We Americans try to do too much extreme sightseeing by hitting multiple cities in too short a period of time. By staying put or just doing two cities, you can also experience the city more plus reduce your stress by not having to pack/unpack, change hotels, and travel in between such cities.
Have fun and here are a few links to get you started.
Starwood Personal:
http://www304.americanexpress.com/ge...&AFFID=k547977
Starwood Biz:
http://www262.americanexpress.com/bu...dit-card/29790
AA FlyerTalk thread:
http://www.flyertalk.com/forum/miles...nks-first.html
UA CC application link:
https://www.united.com/web/en-US/app..._to=thatsaplus
Additional handy sites if you aren't using them already:
http://www.freefrequentflyermiles.com/index.htm
http://www.frugaltravelguy.com/
http://thepointsguy.com/
http://boardingarea.com/blogs/viewfromthewing/