I know the book says the maps are for DM eyes only. However, the Phandalin town map seems like it was meant for the players to see. Am I missing something revealing on the town map or can I show it to my players for sake of immersion? Thanks!
Showing your players the Phandalin town map shouldn't be a problem. There are many locations marked on it, but most of them are useless out of context, and if your players are keeping a journal (and they should) even that extra info doesn't bring an advantage. I've shown my players the whole Phandalin map when they went to explore the town and it has not caused any problems.
Having your players know the layout of any other map, however, will affect the way they play. As much as they try to roleplay it and separate player knowledge from character knowledge, it's hard to get the image of where things are out of your head while it's right in front of you. They will be more biased towards places that look better to them (whether they're actually better depends on the situation).
If you want to show your players a map of a dungeon, what you can do is cover up parts of the map that the players haven't explored yet. In my campaign, I use Roll20 and its "Fog of War" feature. As they progress through the dungeon, I reveal the sections that are within their line of sight. It's a bit fiddly, but my group is completely new to the game so I wanted them to have the extra visual aid, and introduce "theater of the mind" gradually. You could just use a printed map and a couple pieces of paper and move them strategically. It's not as precise but it's faster. Alternatively, you can purchase a Roll20 subscription to get the "dynamic lighting" option and just use a token for your group.
And now that you're hiding parts of the map the players haven't visited, it's time to get rid of all the DM clues and markers. A quick google search for a specific location will usually net you a clean map that you can show to your players. Secret passages are a slight issue, but if you're good enough with the gradual revealing you'll make sure no hints of the passage show until the explorers discover it. In Roll20 I also use the GM overlay to add all the DM hints back for my eyes only, so I can use the Phandlever book to look at other things.
I gave my characters the Phandelin map (or at least the replacement I drew) as soon as their characters entered the town.
I gave them the dungeon maps (Cragmaw Hideout, Cragmaw Castle, Redbrand Hideout, Wave Echo Cave) only once they finished the entire dungeons, so they could look at what the place was like. These maps have secrets on them that I don't want the players to see before they have cleared the area.
Mike Schley's maps (as mentioned in another answer) contain both player's and GM's versions of the dungeons, but the player's versions still show where the passages are, so players can deduce the location of secret doors.