Games with "Visual Novel" tags that have RPG elements?

Hyperdimension Neptunia , Fairy fencer F

Valkyria Chronicles.

Sakura Dungeon

Disgaea

Sengoku Rance

Utawarerumono, Rewrite.

Many of the titles published by Idea factory
Hyperdimension, Fairy Fencer, Trillion, ...

Akiba's Trip
Rabi-Ribi (somewhat)

The Sunrider series. I started playing it and at this point I'm playing it more for the gameplay than the VN elements itself.
Sunrider Mask of Arcadius (Part 1 and part 2 which is free)
Sunrider Liberation Day (Part 3 which is in the 3rd tier of the humble sekai project bundle)

I think Planet Stronghold has battles and a lot of other RPG elements but I never made it far enough to tell for sure. (unrelated to the quality of the game)

I thought the lack of gameplay was what defined them as visual novels.

http://store.steampowered.com/app/291050/
ya.. games made by this company is well known for visual novelish game with some actual combat.
I suggest you start with loren.

Well, it sounds like you are looking for jrpg.

I think it's a western VN-like game, but Dark Scavenger would fit that as well - walking around like in a choose your own adventure map, having events that play in a VN-like "character on screen while talking" way, and having turn based combat which gives majority of the gameplay, while the VN parts give the story and the worldbuilding. The game is a little crude, but if you can get it cheap and otherwise it interests you, it's a genuinely unique, well done game :)

BlazBlue

Sunrider: Liberation Day

Afaik from the Sekai Project bundle which I assume is most of what you're seeing only Sunrider has any kind of battle mechanics.
There's a great deal of anime-styled games out there with gameplay that have nothing to do with visual novels(like most of what has been mentioned here...unless we call VN everything with a story that comes from Japan) but the closest to a "mix" of the two I think would be Agarest(mix of SRPG with multiple conclusions, waifus and every maiden's panties in a twist over the MC)
Although I'd say it still leans a bit too heavily on the rpg part. Off Steam I'd suggest the Tears to Tiara and Castle Fantasia franchises, those are closer to the VN part than the rpg while still featuring battles.

Tomoyo After, it has a seperate dungeon crawler game

Baldr Force.

Many comments here are mixing JRPG and visual novel genres. JRPG is JRPG, it can't be in any way forced into visual novel category and vice versa. With that logic you can call Max Payne a comic-book and graphic novel because of comic-like narrative in those scenes, but... that logic is totally, TOTALLY wrong. Missed point.

God Capturing Alchemy Meister - Turn Based RPG
Yumina the Ethereal - Dungeon Crawling RPG
Sengoku Rance - Turn Based Strategy

brave soul and Demon Master Chris

do you like dungeon n dragon? like novel (book)? lotr style?

then you should try Sorcery 1 - 4, unlike japanese style visual novel, those games are like interactive "book"
http://store.steampowered.com/app/411000/Sorcery_Parts_1_and_2/

If you are into mecha then Baldr series