После обеда мне хочется немного погулять в парке.

После requires the genitive case (the “after/of” form).
So обед → обеда (genitive singular).

• после обеда = after lunch
  Not:
• обед (nominative)
• обедом (instrumental)

Мне is dative (“to me / for me”). With хочется, Russian often uses an impersonal construction where the “person who feels the desire” is in the dative:

• мне хочется = literally “to me it is wanted” → “I feel like / I want”

You generally don’t say я хочется (that’s ungrammatical).

Хочется is:

• the 3rd person singular form of хотеться (a verb meaning “to feel like / to have the urge to”)
• used impersonally (no grammatical subject)
• often paired with dative (мне, тебе, ему…)

So the structure is: (кому?) мне + хочется + (что сделать?) infinitive

Both can mean “I want,” but the nuance differs:

• я хочу = more direct, deliberate intention: “I want (and I choose/plan to).”
• мне хочется = more like a feeling/urge: “I feel like / I’m in the mood to.”

In this sentence, мне хочется sounds natural and soft, like a spontaneous desire.

After хочется, Russian normally uses an infinitive to name the action you feel like doing:

• хочется (что сделать?) погулять This is similar to English “feel like going for a walk.”

Погулять is usually perfective and often means “to take a walk for a while / go for a short walk (and then stop).”
Гулять is imperfective and is more about the process/habit of walking or strolling.

So:

• хочется погулять = “feel like taking a walk (a bit)”
• хочется гулять = “feel like walking/strolling (in general, as an activity)”

Here немного modifies погулять: “to walk a little / for a bit.”

Its placement is flexible:

• мне хочется немного погулять в парке (very common)
• мне хочется погулять немного в парке (also possible, slightly different emphasis)

В парке is prepositional case and means “in the park” (location).
В парк is accusative and typically means “into the park” (direction).

With погулять, you can describe the place where the walking happens:

• погулять в парке = take a walk in the park

Yes, and it changes the nuance slightly:

• в парке = walking in the park (location, general)
• по парку = walking around the park (emphasizes movement “around/through”)

Both are natural; по парку can feel a bit more “wandering around.”

Word order is quite flexible; moving parts changes emphasis:

• После обеда мне хочется немного погулять в парке. (neutral)
• Мне хочется немного погулять в парке после обеда. (emphasis on wanting to walk; time added at the end)
• В парке мне хочется немного погулять после обеда. (emphasis on the park)

The grammar stays the same; you’re mostly adjusting what sounds “foregrounded.”

Yes. Without мне, it becomes more general/impersonal:

• После обеда хочется немного погулять в парке. = “After lunch, (one) feels like taking a walk in the park.”

Including мне makes it clearly personal: “I feel like…”

Key stresses:

• по́сле (stress on по́)
• обе́да (stress on бе́)
• мне (one syllable, often reduced in fast speech but still clear)
• хо́чется (stress on хо́)
• немно́го (stress on но́)
• погуля́ть (stress on ля́ть)
• па́рке (stress on па́)