Some anecdata: I generally do not feel caffeine at all after ~2 hours. This is consistent under all circumstances; whether it's the morning cup puttering out around lunch time or whether it's an after-work latte fading long before I need to sleep.

Honestly, if I'm truly tired I can go to sleep immediately after drinking a cup. I don't generally intend to do this, obviously, but I've never felt like coffee prevented me from sleeping. It gives me clarity and makes me feel invigorated, but it doesn't feel like the opposite of sleep.