Learn Hardcore Russian: Я сравниваю этот город и тот город.

этот = this (close to the speaker in space, time, or topic)
тот = that (farther from the speaker, or something more “remote” in context)

So:

этот город – this city (the one we’re talking about right here / nearby)
тот город – that city (another one, farther away or previously mentioned)

The contrast этот … тот … is often used specifically to emphasize the difference between two things: this one vs that one.

Why is it этот город и тот город and not этот город с тем городом? Which is more natural?

With сравнивать, the most typical pattern in Russian is:

сравнивать X с Y (compare X with Y)
→ Я сравниваю этот город с тем городом.

Your sentence Я сравниваю этот город и тот город is understandable and not wrong, but sounds a bit less idiomatic. It’s more like “I compare this city and that city” just listing two objects.

If you want the most natural, textbook-like Russian, prefer:

Я сравниваю этот город с тем (городом).

Note that in that version:

с тем городом is in the instrumental case (тем городом) after с.

What case is город in here, and why does it look like the dictionary form?

Город here is in the accusative singular (direct object of сравниваю).

For inanimate masculine nouns like город, the accusative singular form is identical to the nominative singular form:

Nominative: город (city) – used for the subject
Accusative: город – used for the direct object

So it looks like the dictionary form, but grammatically it’s accusative.

A quick mini-paradigm (singular):

Nom.: город
Acc.: город
Gen.: города
Dat.: городу
Instr.: городом
Prep.: (о) городе

What about the case of этот and тот in this sentence?

Этот and тот agree in gender, number, and case with город.

Here:

город = masculine singular, accusative
It is inanimate, so the accusative = nominative

Thus:

этот город (this city) – masc. sg. acc. (same form as nom.)
тот город (that city) – masc. sg. acc. (same form as nom.)

If the noun were animate, the masculine accusative would look like the genitive:

Nom.: этот студент (this male student)
Acc.: этого студента (I see this student → Я вижу этого студента)

Why is it я сравниваю and not я сравню or я сравнил?

Russian verbs come in aspects:

сравнивать – imperfective (ongoing, repeated, process)
сравнить – perfective (single, completed action)

Forms:

я сравниваю – I am comparing / I compare (right now, or habitually)
я сравню – I will compare (one-time, in the future)
я сравнил – I compared / I have compared (completed past action; masculine speaker)

So я сравниваю here expresses an action in progress or a general activity, matching English “I am comparing” or “I compare” depending on context.

How can я сравниваю mean “I am comparing” if there is no separate continuous form in Russian?

Russian doesn’t have a special continuous tense like English am doing. Instead, the present tense of an imperfective verb (like сравнивать) can mean:

a process happening right now:
Я сравниваю этот город и тот город. – I am comparing this city and that city (now).
a habitual or repeated action:
Каждый раз я сравниваю этот город и тот город. – Each time I compare this city and that city.

Context tells you whether to translate as “I compare” or “I am comparing.”

Can the pronoun я be omitted here?

Yes. Russian often drops subject pronouns because person and number are clear from the verb ending.

Я сравниваю этот город и тот город.
Сравниваю этот город и тот город.

Both are grammatically correct.
The version with я can feel more explicit or slightly more emphatic (“I am the one comparing…”), but in neutral speech, omitting я is very common.

Is it necessary to repeat город: can I say этот и тот город?

You don’t have to repeat город. All of these are possible:

Я сравниваю этот город и тот город.
Я сравниваю этот и тот город.
Я сравниваю этот город и тот.

They mean the same thing. Versions 2 and 3 sound a bit more natural in everyday speech because Russian often avoids unnecessary repetition when the noun is clear from context.

Is the word order fixed, or can I move things around?

Word order in Russian is relatively flexible and is used for emphasis. All of these are possible:

Я сравниваю этот город и тот город. – neutral.
Этот город и тот город я сравниваю. – puts emphasis on these cities as the topic.
Этот город я сравниваю с тем городом. – emphasizes this city more strongly.

The basic information stays the same; what changes is which part is highlighted.

How do you pronounce сравниваю, and where is the stress?

Stress is on the first syllable:

срáв-ни-ва-ю

Pronunciation tips:

срáв- – the а is clear and stressed.
-ни- – short, unstressed и.
-ва- – the а is reduced and sounds closer to a weak “uh.”
-ю – [ю] at the end: “yu”.

Altogether: roughly SRAHV-nee-vuh-yu (one smooth word).