There are two types or r, the trilled r and the uvular r. Both are "German", though the latter is used more in the north, and the former more in the south.
The r can become quite weak at the end of the word or before some consonants, but the tendency to change it into "a" as miodisen describes it is VERY Northern German.
Don't worry about the pronounciation too much, just keep using the r you are already using. You will be understood just fine, and it won't sound strange. For Americans, it's much more important to use "flat" vowels and get rid of the "twang". :-)