On all versions of Zelda Classic 2.10 and below, the Classic Tileset is screwed. I took it into my own hands to use the 2.11 betas as a base and recolor the Classic Set, since the betas feature the correct palette. In other words, I recolored it so you don't have to.

Package includes the Palette file and the Graphics Pack file, as well as the original First Quest with the palette applied to it.

EDIT: People are commenting that there are no new tiles in this set. The point of this set is a perfect recoloration of the Classic Set. Just look at the title. There are not any new tiles because this isn't meant to have new tiles. Thanks to LinktheMaster for adding this in for me.

UPDATE: due to popular demand, I have downgraded it to 1.90. The package still includes the graphics pack, the palette file, and the 1st quest with the revised colors. Only now, it works in all versions 1.90 and up.

2nd UPDATE: Reupdated thanks to Radien with some new pics. There are six pics, but two different versions of three different ones. Also, I've checked, and have also been alerted, that the .zgp doesn't load on some versions, so my advice to you all is:

IF THE .ZGP FILE DOES NOT WORK, PLEASE USE THE .QST FILE, WHICH WILL WORK

Pics:
1-2 - A pic out of ZQuest of the top-leftmost screen. First pic is my tileset, second is old.

3-4 - The opening screen where Link is. Here, you can see how the new colors affect Link himself, as well as shades of other colors. Watch the subscreen between the two pics. Again, first is my tileset, second is old.

5-6 - The screen outside of level 1. You can see the differences between the two sets much better in this shot. Once more, the first pic is mine, second is old.

Old-Skool, Moonwhisper, and Radien suggesting I go for it
Nintendo for making the Classic Set
The ZC Developers for creating the system
Myself for editing every single palette to perfection

As of 2nd update: Thanks to Radien for suggesting a new update that shows the differences between the pics.