I have just returned from Turkey and was talking recently to a friend about their upcoming visit to Europe and thought I'd pass along some ideas to get more out of your trips, stateside or overseas:
Try to find books, movies and TV shows set in or about where it is you're traveling to; better yet, find those which are actually made in where you're going.
Go to iTunes and check out the Podcasts, iTunes U offerings, iBooks etc. Rick Steves has both audio and video podcasts that provide loads of helpful information, as do many others. Put the city or country name in the search field and see what you find.
Go to the App Store part of iTunes and do the same: find iPhone/iPad apps that are travel guides or other helpful apps about the place you're going to. I am sure Amazon has a similar feature for Android phones.
Put your itinerary details in PDF form and upload to your Dropbox, Evernote account, or wherever you maintain your cloud presence. That way, if you need the details but you've lost the papers, you can find and download them whereever you are.
Go to iTunes and find the Radio selections and see if there's music from the country for you to listen to. Then you can buy and bring back a CD of the country's music if it strikes your fancy.
I'll go thru my iPhone & iPad and see if I can suggest specific apps I've found helpful, but this is a start, perhaps.