I could try to make the English rhyme.

But today I didn't have the time.

I hope I've helped you in some way.

If not, I'll try another day.

Corrections in red.  Stylistic suggestions in blue.

Good Evening, Moscow.

(This is a part of a beautiful song... but actually this is my next battle with "THE" and "A":)

Good Evening, Moscow.

Good evening, my city, which was bewitched by spring.
City-jazz, city-blues, city-rock-'n'-roll.    
City of songs and poems, of quiet parks, of old walls,
I have come to stroll with you this night.
Mysterious lights are glowing along alleys and boulevards.
The rain is ambling along the sidewalk, we are alone with it on the street.

Hey, city, hey, don't regret the diamonds, 
How many of them in the lanterns' dance. 
The leaves are whispering unintelligible words.
You are my city, Moscow.


Добрый вечер, Москва.

Добрый вечер, город мой, околдованный весной.
Город-джаз, город-блюз, город-рок-н-ролл.
Город песен и поэм, тихих парков, старых стен,
Я с тобой в эту ночь побродить пришёл.
По переулкам и бульварам горят загадочно огни.
Гуляет дождь по тротуарам, мы с ней на улице одни.

(припев)
Хэй, город, хэй, бриллиантов не жалей,
Сколько их в танце фонарей.
Шепчет листва непонятные слова,
Это ты мой город, Москва.