Arkansas appeared in various bowl projections sporadically this season, but they largely fell out around mid October when things were looking a bit dim. However, those days are long gone and now that Arkansas is officially bowl eligible, they're in all of them.
We discussed this immediately after the Ole Miss game, but I think the Liberty and Independence Bowls are the most likely landing spots for Arkansas. If the Hogs beat Missouri, they probably end up in the "Pool of Six" which include the Liberty, Music City, and Texas Bowls. They may still land there even with a loss to Missouri but the Independence Bowl might also be in play.
If there's a bowl to avoid, it's probably the Birmingham Bowl. It's after New Year's (January 3rd) in a bad stadium against an AAC team (likely Memphis). I think there's a good chance that's not a problem, though.
Without further ado, this is where most of the experts have pinned the Hogs.
SB Nation: Liberty Bowl vs West Virginia
ESPN: (Mark Schlabach) Liberty Bowl vs West Virginia, (Brett McMurphy) Music City Bowl vs Penn State
CBS Sports: Liberty Bowl vs Texas
FOX Sports: Liberty Bowl vs Texas
Yahoo!: Liberty Bowl vs West Virginia
Sports Illustrated: Independence Bowl vs North Carolina
Phil Steele: Liberty Bowl vs West Virginia
As you can see, the Liberty Bowl is the heavy favorite, and would be sure to spark plenty of silly "Bielema and Petrino both went to the Liberty Bowl in Year 2!" discussions.
I will say this though, if Arkansas does face Texas in the Liberty Bowl, that would be SO AWESOME.