I'm not an expert, but I looked into this recently when toying with the idea of a scale model of the observable universe. To the best of my understanding, the following is approximately correct.
TLDR: The expansion happens on the very large scale of the universe. At the scale of the observable universe the Andromeda galaxy is a next-door neighbour, and at the local scale gravity is strong enough to override any effect of expansion.
The Milky Way is 100,000 light years across, 2.5 million light years brings us to the Andromeda galaxy.
Galaxies cluster in galaxy groups, and 10 million light years span about 50 galaxies and brings us to the edge of what's called the Local Group.
Galaxy groups cluster into superclusters. We're part of the Laniakea Supercluster, which spans about 100,000 galaxies and 500 million light years.
For any appreciable expansion (redshift 0.1) you need at least a billion light years. It's something that happens in the voids between superclusters, and doesn't become really pronounced until you're halfway across the observable universe (redshift 1, 7-8 billion light years as measured in light travel time).
For the "raisins in a loaf" analogy, I think it's not too wrong if you think of the raisins as superclusters rather than individual galaxies. Note that although the dough expands in a baking loaf, individual raisins do not, because there are other forces at work that hold them together.