Well, are you thinking of cashing in all the points/miles for this one trip?

I'd suggest visiting one country (at least) in each continent on your first trip if you haven't traveled much in the past. Example:

1) AA business one-way to South America from N. America 50K miles
2) AA business one-way to Oceania from South America 50K miles
3) AA business one-way to S.Asia from Oceania 35K miles
4) UA one-way business to N. Asia from S. Asia 15K miles (rate changes on June 15th)
5) UA one-way S.Africa to Europe in F (50K miles - I think this is a bargain!)
6) AA business one-way back to N.America 50K miles in business

So, this in total would cost you:

* AA - 185K miles (a bit over what you have, but on one of the itineraries, you can easily switch to BA miles)
* UA/CO miles - 65 miles (transfer some of your AMEX MR to CO and then to UA)

You'd still be left with 100K BA miles + 60K AMEX MR, which would still be good enough for another nice trip.

Just to note that S.America to Oceania award in business is difficult to come by.