Can I progress in storyline without doing dungeons?

[Niwashi]

You want things to be handed to you. Spoon fed if you will. The bread and butter of ALL MMO's I to grind dungeons for gear. If you can't get with that, I'm pretty sure there's a few copies of LR:FFXIII out there for you.

It's the bread and butter of this MMO, but not all of them. Some actually have enough content that you don't have to keep repeating the same dungeons over and over unless that's what you like to do.

LOTRO, for instance, has tons of content. I played that avidly from the time it released in 2007 until FFXIV:ARR came out last year, and I never came anywhere near to running out of content. Now, that's playing with nine main characters (as well as several lesser-played alts), and doing all the regional quests, plus spending time on crafting and other activities. Many other players stick with just the main storyline, skipping all the optional stuff, and they might reach endgame within a couple months. It depends on how you want to play it. It has endgame raids for players who like that, but it also has tons of questing for people who prefer that. And (particularly with a few alts) it's easy to stay busy for years on either sort of content.

ARR, in contrast, is much more limited. It's still a great game, and I think it's a lot of fun, but it's only fun if you go with the pattern it's designed around. It lacks the breadth of content that allows a game like LOTRO to cater simultaneously to a wide range of players.

[Gnova]

It's the bread and butter of this MMO, but not all of them. Some actually have enough content that you don't have to keep repeating the same dungeons over and over unless that's what you like to do.

LOTRO, for instance, has tons of content.

Yes lotro has lots of content, it's been out forever and had a fair number of expansions. In the early days there was next to nothing to do at level cap.
Lotro is a very grindy game. It has kill 90,000 mobs in the lore challenge book (can't remember it's name) and you will kill mobs for hours and hours in order to farm mats for crafting.
You say there isn't a end game grind but that is only because you have chosen to level a pile of alts and do the same content over and over again.
I've got a lifetime sub to lotro but never play it because it is too grindy even for me.