[Grammar] like to do/ like doing

Can we use "like to do" and "like doing" interchangeably?

Where do you like to go on holiday?
I like to go on a beach holiday in the summer.

angelene001 said:

Can we use "like to do" and "like doing" interchangeably?

Where do you like to go on holiday?
I like to go on a beach holiday in the summer.

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Your title and first line question ask about the interchangeability of "like to do" and "like doing".
Your example sentences use "like to go" and "like going".

Which one would you like us to deal with?

I'm sorry. I'd like to ask about "like + gerund" and "like + to-infinitive" in general.

I've always been taught that we use "like + gerund" to talk about things, activities we like.
I like watching TV.
We can use "like + to-infinitive" to talk about things which we think are good to do. For example:
I like to exercise twice a week.

When I see such an example, I'm confused:
- Where do you like to go on holiday?
- I like to go on a beach holiday in the summer.

There isn't really a difference in meaning like with some verbs which can be followed by both gerund and infinitive (such as stop, remember, forget), the difference is more in the context you are describing. I found an old thread with the same question and Tdol puts it well here: https://www.usingenglish.com/forum/...ke-doing-i-like-do-differences.html#post12058

Consider these:

1. I don't like to disturb her. (I don't want to)
2. I don't like disturbing her. (which I've done/ I do, I don't enjoy it)
3. I love skiing/ to ski in the early spring. (which I've done/ I do, I enjoy it)
4.I prefer staying/ to stay in on cold winter evenings (which I've done/ I do).

When you use like (or a few other verbs such as prefer, love, hate) with the infinitive, it means you have feelings beforehand about what may happen.* Then the meaning of the verb is (not) want. See example 1.

*What does happen depends on circuimstances. I don't like to disturb her, and so I'll call her later/ but I'm afraid I must.

When our feelings accompany or follow what happens (or what we know will happen), so that the meaning is (not) enjoy, these verbs take -ing or the infinitive (when affirmative). See examples 2, 3 and 4.

Source: H. Gethin, Grammar in Context