I'm placing a hot tub in my back yard, so I'll have to pull electrical out to it. While I'm there, I plan to place some outdoor outlets and string some accent lighting. Can I pull 10/3 wire from a 30 amp breaker from my main breaker box and run it to a main lug for outdoor distribution? Or do I have to run something thicker, with more amps? Thanks

That depends on a couple things.

What is required for the hot tub?
How many lights and how many watts will each bulb be?

And how far away it is.

Most hot tubs require a special 240 v GFCI 50 amp breaker and outside disconnect. Check with your building department to be sure what they will inspect for.