What can I bake for my nut allergic friend?
Step 1 should always be to ask  which ingredients exactly you need to stay clear of, just in case it's more than nuts.

My - possibly naïve - assumption would be that basic recipes that stick to flour, sugar, eggs, butter and possibly dairy should probably be ok. Chocolate could be dangerous as the factories often use nuts as well, so there is a risk of cross-contamination, but cocoa should be safe. Note that some oils can be made (partly) from peanuts, so read the label or use butter.

Once you have verified the extent of allergies, you will have a "safe ingredients list". 

From there, choose the type of baked product and search for basic recipes - the no-frills, few-ingredients recipes are a good place to start. 

Unless you choose a recipe that uses nuts as main ingredient (sorry, no macarons for your friend) the options are almost endless, in my experience.