The Honorverse certainly fits the description - there is FTL spaceflight (riding gravity waves using Warshawski sails or wormholes - sublight travel uses a related gravitic drive called an impeller) but communication either inter- or intra-system is limited to lightspeed. And a similar restriction applies to some of the ship-to-ship weaponry using lasers and gamma ray lasers (grasers) - to paraphrase (since I can't remember the exact quote and I haven't got the books on my Kindle yet)
grasers were a light-speed weapon - the first you knew you were being
attacked by one was when you got hit
There are FTL sensors, however, since gravity is ruled to propagate faster than the speed of light, allowing for the detection of ships using their impeller drives, and as the series of books progresses a crude FTL communication method develops for use in-system, using sensor drones equipped with gravity emitters; however the gravity emitters can only generate 'pulses' at a slow rate, and so the drones can only emit, at best, a kind of Morse code. The limited range (in an interstellar context) of gravitic sensors makes this impractical for use between systems.
This lack of inter-system communication (except by, as you say, FTL courier) becomes an important plot point in several of the books, for example in The Honor of the Queen where the only way to send for reinforcements is to despatch a courier to a neighbouring system and then hope the cavalry arrives in time...