Although I travel the entire breadth of the wine world, I have a special fondness for contrarian wines, and the most contrarian of all wine categories is "off-dry." Sweet wines can sometimes get by as "dessert wines," but anything that falls between dessert wine territory and deepest, darkest cabernet sauvignon is considered trash by the wine snobs, and gets no respect and no press. (Still, despite all their efforts, white zinfandel remains the most popular wine in the US.)
I'm a sort of wine philistine, and while I have my likes and dislikes, none of them have anything to do with wine ideology. If I think it tastes good, that's all I ask, and I don't try to make universal principles out of my taste peccadilloes. For example, something about sourness in wine is a turnoff to me, which is why I don't like whites as much as reds. (Whites tend to have more acid and taste sour to me.) Nor do I favor taste/scent nuances like "earthy," "smoky," etc. Wine is made from fruit and should taste like fruit, not like iron nails, burning cork, or dark green leafy vegetables. (We won't even talk about cat urine.) That said, I truly hope that your mileage varies; there's no point in all of us liking all the same stuff all the time.
Few wines dare say "off-dry" on their labels, and I typically buy the bold exceptions. One reasonable wine in this category comes from Moldova, where they apparently don't care that much about American wine snobs. Garling Collection's Black Monk red wine comes in a distinctive three-sided bottle, and is a shade less sweet than white zin, but still much less dry than a conventional merlot, pinot noir, or red zin. My only discontent is that the wine has a sour edge, rather like those cherry-flavored sourballs that were popular fifteen or twenty years ago. Nonetheless, it's very fruit-forward, very smooth, and extremely drinkable. Much more body than white zin, and not quite as sweet. It's not very expensive ($8-$10) and I've seen it in a number of places, so you should be able to find it around. If conventional red wines taste too dry to you, give it a shot.