If you create an (free) account at: https://db.humanconnectome.org , I believe you should be able to find connectomes through here.
It seems like a bit of a hassle to download the files though (and they only seem to come in very large packs).
Another perhaps easier method, if you just want some simple and easily accessible files to work with right away is:
which you can read more about in this article.
There you can just download some graphs directly in .graphml format. Then you can use them in e.g. python with networkx. For example, to construct a graph object from a graphml file, plotting it and getting the adjacency matrix, you'd simply write:
import networkx as nx
G = nx.read_graphml("/rhesus_brain_2.graphml")
M = nx.adjacency_matrix(G)
nx.draw(G, node_size = 10, width = 0.1, arrowsize = 2, pos = nx.spring_layout(G))
This is just a simple example, but I hope it helps. It sounded as if that was perhaps just what you needed: something raw and simple to get you started; and those datasets are sometimes the hardest to find.
(I am myself on the lookout for more specific types of connectomes; see my question here. If you happen to come across anything more, I'd be really grateful if you'd let me know.)