I want to save juicy tomatoes, but not in freezer. How might this be possible?
Tomatoes can last that long in a root celar at 15 degrees Celsius. You have to choose tomatoes bred for lasting - so supermarket ones, not homegrown heirloom varieties, and preferably not perfectly ripe and juicy. Your biggest problem would be mold, so carefully check each tomato for places where the skin is torn or the tomato has been squished. Then carefully order them such that there is enough air/ventilation around them, ideally in a single layer. If the humidity around a tomato gets too high, it will grow mold at the place where it grew out of the wine. And never let the temperature drop below 13 Celsius (so don't do it in the fridge!) because they change their taste then.
If you cannot do that - for example, if you just harvested a large amount of overripe tomatoes and wonder how to not lose them - your only option may be making something out of them that can be canned.
There's no point in freezing tomatoes. Freezing tears their delicate innards to shreds and they thaw to an unrecognizable mess. Stewed tomatoes can be bottled but the texture is not similar to fresh, of course.
20 days is approaching the longest I've personally every had tomatoes last in the fridge. It's a long shot but the fridge is really your only choice. Tomatoes are just fragile fruit that should be eaten quickly.
Tomato preservation methods are bottling, drying, or making sauce. All of these destroy the delicate texture.
I don't know if you can get 20 days out of them without refrigeration, but there was an episode of Tyler's Ultimate where he was in Italy and claimed that there were tomatoes that had been preserved by smoking, but of the many discussion boards, I'm not aware of any that have been able to confirm that he wasn't just giving bad information. See https://www.chowhound.com/post/smoked-tomatoes-293900
To get your tomatoes to last longer at room temperature, you can get a day or two more out of them if you store them stem-side down.
As my step father grows a lot of tomatoes, my mom will typically go through them every day or so, pulling out the ones that are starting to soften up to use that day, or if there are a lot, to make into a batch of tomato sauce. As they're constantly refilling, I doubt any of them are sitting there for 20 days.
I don't even know if you could get 20 days with refrigeration unless you are rather specific about the type of tomatoes (plum and smaller tomatoes tend to last longer, but I'd add paper towels to absorb moisture so they don't start developing mold.) I'd also avoid store-bought tomatoes, as those might already be a week old. Serious Eats mentions that refrigeration isn't so bad, so long as you let it get back up to room temperature before eating.