NowadaysRecently, the weather hasn't been good so I often go to a laundromat to dry my clothes. Recently, the weather hasn't been good so I often go to a laundromat to dry my clothes.

"Nowadays" is mismatched with "hasn't".

NowadaysLately, the weather hasn't been good so I often go to a laundromat to dry my clothes. Lately, the weather hasn't been good so I often go to a laundromat to dry my clothes.

I like the laundromatit there because it is a good place forto reading. I like it there because it is a good place to read.

I have to wait for twenty to thirty minutes while my clothes driedy, and the time is good enough forto reading a bunch of a few pages. I have to wait for twenty to thirty minutes while my clothes dry, and the time is enough to read a few pages.

Or "until my clothes have dried". "good enough" (i.e., sufficiently good) is not correct here. "a bunch of pages" sounds weird to me.

I usually have to wait for twenty to thirty minutes whuntile my clothes are dried, and the time is good enough for reading a bunch ofwhich gives me enough time to read many pages. I usually have to wait for twenty to thirty minutes until my clothes are dried, which gives me enough time to read many pages.

BesidesMoreover, the sounds of coming from the washing machines areis just like white noise. Moreover, the sound coming from the washing machines is just like white noise.

Consider "background noise" instead of "white noise". "are" (plural) is mismatched with "white noise" (singular).

BesidesFurthermore, the sounds of washing machines arespinning is just like white noise. Furthermore, the sound of washing machines spinning is just like white noise.

I deleted "besides", because it represents "aside from", or "other than", and I don't believe that is what you meant to convey.

The only downside is that it's bothering to bring wet andsome to carry around wet, heavy clothes. The only downside is that it's bothersome to carry around wet, heavy clothes.

while "wet and heavy clothes" is correct, it's ambiguous: are there two types of clothes ("wet clothes" and "heavy clothes")?

The only downside is it's bothering to bring wet and heavy clothes. The only downside is it's bothering to bring wet and heavy clothes.

If you are drying your clothes at the laundry mat, then why do you have to bring back wet and heavy clothes? Your sentence needs an object. "It's bothersome (not bothering) to bring wet and heavy clothes ....." is not a complete sentence. In other words, where are you bringing the clothes to?