I want to run an Avails Report to see how much inventory is available, but is there a way that I can see what campaigns are getting what inventroy in the same date range?

Yes!  The Inventory Availability Report includes a variable named Contending Impressions.

If users opt to enable Contenting Impressions by checking the proper selection box, then once the Avails Report loads, users will be able to see how much inventory is already allocated and how much is remaining.  And, if they expand the Campaigns Running in Report Date Range section of the screen, there will be a column that details how many impressions each campaign will “take” during the date range the Avails report was run on.  This Contending Impressions column will allow users to gauge which campaigns are taking the most impressions in the specified date range so that they can make any needed adjustments which will allow new campaigns a better chance of clearing.