Yes I agree your location can dictate who you 'hate' the most. Notts is a long county and those in the North Nottinghamshire towns like Retford and Worksop are much closer to Sheffield than the city of Nottingham and there's the whole miner's strike history there too.
Having lived in several parts of the county and having followed Forest for 40-odd years I'd say if you were to do a poll now amongst every Forest fan you'd find that the large majority see Derby as our biggest rivals and take more joy seeing their demise than any other club.
Then there's yourselves, Sheffield United (but not Wednesday), Wolves, Liverpool (for those fans from the 70s/80s) and then I suppose Notts County. I actually like to see Notts do well as it's good for the city generally to have two clubs on the up but some Forest fans would prefer to see them fade into insignificance. Partly due to their hatred towards us and there's also a lack of gratitude there. When County have been in the absolute shite on and off the pitch Forest have made efforts to help them out only for their former fool of a chairman Alan Hardy to try and drum up a rivalry between the clubs by having a pop on twitter, I'm not sure Forest have sent a player on loan there since. Don't bite the hand that feeds you...
I do think these things can be dynamic though and a lot depends on circumstances. If Forest and Leicester both spend years playing each other in the Prem that could be the new de facto EM Derby. If County suddenly started doing well and playing us more then a real rivalry might develop there too.