Joe,
The Simmons 44 Mag scope in the 6.5x-20x magnification costs around $150. As such, it's going to be difficult for me to recommend any other scope, in that magnification, for around the same price.
Most of the scopes that I have personal experience with in the 16 to 24x range are the Bushnell Elite 4200s, Nikon Monarchs, Nightforce NXS, Leupolds, and a few others that I can't really think of off of the top of my head. However, all of these are well over $150. This is not to say, however, that they are not worth the extra money. Most of these scopes are double the price, but, in my opinion, triple the value.
The closest scope that I would recommend, if you are willing to go up to only 15x, is the new Bushnell Legend. I don't know how much they cost, but I believe that they are between the Elite 3200 and the Trophy. As such, you would pay more than what you want, and have less magnification that what you want, but get much better optics and durability.
Like I said, it's hard for me to recommend the Simmons 44Mag scope, but if you are limited to around $150, then you might just go ahead and purchase it. If you do, then please let us know how it works out for you. :grin:
Zachary