I was issued a 1099 MISC form and was required to travel several times throughout the year. Unfortunately, I misplaced several hotel receipts. If I have corresponding receipts, i.e. airline, rental car, and miscellaneous receipts, that prove that I did travel and can establish length of time away from home, is there any way to still claim the hotel expense? Is there a "standard deduction" for lodging like there is with meals and entertainment expenses? Any help is appreciated...

Yes, you can claim the hotel anyway, as long as the hotel costs are not unusually high.