My wife's father currently owns an apartment in St. Petersburg, Russia. He is looking at selling it later this year and transferring the money to me and my wife's account here in the U.S. The amount would be around $150,000. It would be considered a gift. Are there any tax implications for us or him in transferring the money? Or would we need to set up a foreign bank account to receive the money?

The only thing you need to worry about is:

a) ensure you have copies of the bill of sale and other items related to the sale
b) when transferring the money from Russia to the U.S. ensure you don't try to circumvent any financial institution reporting guidelines (i.e. transferring the money in batches under $10,000 or withdrawing the money from your account in a similar fashion).
c) when your bank asks you the source of the funds (believe me, they will since its coming from a high risk jurisdiction), tell them the truth and let them know you have supporting documentation if they require it

Hope this helps.