I believe that the construction of such a centre would undoubtedly contribute to the improvement of our quality of life.
I believe that the construction of such a centre will undoubtedly contribute to the improvement of our quality of life.
Both are correct, but the first one implies that the construction of the centre is just a proposal and suggests that it won't necessarily go ahead (even though, in the speaker's view, it ought to). The second suggests that the proposal has been agreed or is likely to be agreed. (Some speakers also use "will" to pre-empt the decision by sounding confident that it will go their way.)
Organising family-oriented activities would significantly increase membership and raise the society's popularity with the local community.
Organising family-oriented activities will significantly increase membership and raise the society's popularity with the local community.
Again, both are correct, but the first describes what the consequences of the proposed activities would be (if they were to go ahead), while the second describes what the consequences will be (either knowing that the proposal has been agreed or opting to assume that it will go ahead).
We could also express these two sentences like this (respectively):
If family activites were organised, they would significantly increase membership and raise the society's popularity with the local community.
When (or if) family activities are organised, they will significantly increase membership and raise the society's popularity with the local community.
In the if-less and when-less versions of the two sentences, the conditions become less explicit. Where "would" is used, the conditional nature of the statement is still clear. Where "will" is used, the statement sounds more like a prediction, but is still implicitly premised on the family activities going ahead.
