Are you trying to visualize data or run an analysis? Neither should be impacted by your internet connection speed.
Even large data can be uploaded through FTP on slower connections (use Filezilla, and if/when a time-out occurs, just resume the transfer).
If using a genome browser (Trackster, UCSC, IGV, there are many options), regions can be specified for visualization.
For most analysis, it is best to map across the entire genome first, then focus on a smaller region (a particular chromosome or part of one). How to filter for just a specific region depends on the analysis/tools/data formats, but Galaxy has many tools to subset/filter data for the most common types of formats. Try a tool search by the datatype to find these.
Hopefully this helps but if not please describe what you want to do in more detail. Thanks, Jen, Galaxy team