Over the time of our trip we visited four cities.

[Anna232]

Over time of, cramp, buff

I am talking about a trip to Europe. Is "over the time" idiomatic in my sentence?

1. Over the time of our trip we visited four cities.
2. We had to walk a lot so at the end of the day one of the tourists had (a) painful cramp in this leg. Is "cramp" countable in AmE?
3. I met my friend. She is a painting buff. I mean she is an art buff but she loves painting more than any art form.
4. (The) Next day after (the/our) arrival we did sightseeing. I think it would be wrong to omit "the" and either "the" or "our".

 

[Tarheel]

1. While we were there we visited four cities. OR We visited four cities while we were there. OR On our trip to Europe we visited four cities.

2. We had to walk a lot, so at the end of the first day one of the tourists had a cramp in his leg.

3. My friend is an art lover. She especially likes painting.

4. The the day after our arrival we did some sightseeing.

 

[Anna232]

1. While we were there we visited four cities. OR We visited four cities while we were there. OR On our trip to Europe we visited four cities.

2. We had to walk a lot, so at the end of the first day one of the tourists had a cramp in his leg.

3. My friend is an art lover. She especially likes painting.

4. The the day after our arrival we did some sightseeing.

Could you tell me if "the next day" is ungrammatical?

 

[5jj]

The next day we went sightseeing.
The day after our arrival we went sightseeing.
The next day after our arrival we went sightseeing.

 

[tedmc]

Over the time of our trip

There is no such phrase in English. If you are doubtful about a phrase, use something simpler.
You can say "during our trip".