Personally I only really use the NEBuilder tool for designing primers for Gibson Assembly but I know other people in my lab use the double-digest finder for restriction cloning.
Primer BLAST is my favorite tool for primer design since it checks for primer specificity against a given genome:
https://www.ncbi.nlm.nih.gov/tools/primer-blast/
addgene.org isn't really a tool, but it's my go-to when I need to find plasmid sequences since they also carry maps/sequences even for plasmids they don't have in their physical repository.