I thought the Ender's game universe was interesting with the instantaneous FTL communication with the ansible, but no FTL travel. They had some tech that could accelerate ships quickly to very near-light speed, which meant you could travel between planets in a few weeks ship-time thanks to time dilation, but years would pass for the people on the planets. So while you could talk with people on other planets instantly, if you wanted to visit them, they'd have to wait decades for you to arrive.
Then later in the books they figured out ...
spoiler
that you can more or less travel FTL instantly to anywhere you want just by thinking really hard about it.
The Conquerors trilogy by Timothy Zahn had the opposite - FTL travel but no FTL communication. Smaller ships could also travel FTL faster, so you had a bunch of small ships running around to different star systems essentially delivering the mail. It's been a while since I read the books, but I don't really remember it playing a big part of the story other than a way to isolate the battlefronts because once the mail service gets shut down by the enemy you have absolutely no idea what's happening outside of your local star system.