It is important that you save your Google Reader subscription list before the service shuts down on July 1st ! This can be done with Google Takeout. Do it as soon as possible !!
The interesting part is the subscriptions.xml file, which is an OPML file.

The next version of Vienna will support the "Open Reader API", allowing synchronization through services supporting it.

Bazqux and FeedHQ are the services I am currently testing with, and we made significant progresses in the last 48 hours. I'd like to thank Vladimir and Bruno for being so open-minded regarding interoperability and for their help.
Bazqux and FeedHQ are also supported by Mr. Reader (iPad) and Feeddler Pro (iPhone).

If you prefer to wait before subscribing to a sync services, you can have your feeds set locally :
- save your Google Reader subscription list as described before,
- in Vienna Preferences, uncheck "Sync with Google Reader"
- To avoid duplicates, delete all feeds/folders marked with "[G]"
- use the "File->Import Subscriptions…" menu item and select the subscriptions.xml file