I am travelling throughout Europe (Eastern and Western), as well as
Australia, later this summer / fall.  I would like to arrange meals,
bike rides, tours, etc. with "natives" of the countries I am visiting.
Ideally, my companions would be other singles in their 20s (like me).
I want to go to the cool places and meet cool people, on a
pre-arranged basis to the extent possible.  Are there any resources
(offline or online) that could help me set this up?

I'm not a researcher, but if you're going to FRANCE, you might try
reading/posting an ad on www.fusac.com   France-USA Contacts.  It's a
newspaper and website that lots of people use to hook up from
everything from apartments to meetings to jobs.

www.craigslist.com now has a page for LONDON.  And ads are free to
place and/or answer.  The U.S. Craigslists are used mostly by hip
20-somethings, so I would bet the London one would be, too.

This may be a long shot -- could be too sedate or square, especially
since you're looking for cool people to do cool things, but one of my
travel guidebooks says, "Tourist office in some cites abroad keep
lists of local people who are willing to meet with visitors.  One
longtime program exsists in Zurich, c/o the Zurich Tourist Office. 
Another is in Brussels, where the Chatterbus tour organization has a
list of English-speaking reidents who will either join you on foot or
drive you on a sight-seeing tour of the city, free of charge.  The
French tourist office also maintains a list of organizations that
foster visit."
Maybe you could try typing "meeting local people abroad" and
permumtations of that in Google.

No sooner did I post the message above, then I noticed the the BANNER
above your question and Google itself has a sponsored link based on
the topic of the question:  www.travelchums.com    I took a quick
look.....has a lot of stuff you can access for free, if you don't want
to pay to be a member.

If, by any chance, you are a member of Mensa, be sure to contact the
SIGHT Coordinators in the places you plan to visit. This is an
excellent way to connect with folks anywhere in the world.

http://hkmensa.org/sight.htm