<p>Ok the number helps 
Indeed financially speaking you can aim for most colleges now, without financial aid, and STILL apply for merit in some places.
Yes, I would recommend GWU. As has been noted above, I would also recommend Fordham (in NYC). Perhaps Villanova (in Philadelphia), Goizueta/Emory (in Atlanta) as well as Georgia Tech (also in Atlanta and not JUST for engineering, their business programs are very good), definitely Carlson/UMN in the Twin Cities (home to more Fortune 500 headquarters than most anywhere else + very cool city), a couple UC’s (not UCB, UCLA or UCSD, since you wouldn’t have a high enough GPA, but UCSB, UCD, or UCI would totally be in the cards.)</p>