Stability in general,.free movement (to tourism, educational opportunities, culture in all its forms1). There's money involved in those, but only in the way that money is always involved.
Being part of a power-block (and with more say as to how that powerblock works than we would by bunking up in Trump's cell) was very important. And just like Cornwall doesn't always have the same priorities as Lincolnshire or Cumbria or Kent, just because we're not always happy doesn't mean we (or Cornwall) would be better off out of Europe (or UK/England, depending upon the scheme).
Much of the Brexit was money (that infamous £350m for the NHS, etc, that was almost immediately disavowed), and the rest could as easily be linked to money as the non-monetary Remaining stuff.
e.g. those EU seasonal workers undermining our own workforce, not that we seem to have an appetite for seasonal work (and our benefits system strongly discourages it!), meaning that we need to pay more to our reluctant workers (and no more EU subsidies for environmentally friendly land use, unless we decide to fork out from our national purse directly, as on of many potential costs we didn't previously have), meaning food prices rise (or general taxation), hitting everybody who wants to eat (but not actually scaling to their wealth bracket, so richer people will be fairly Ok with that, our homegrown workers less so, unless somebody actually changes the benefits system to pay out more money to the low end(!)...).
But it was the bus and the (non-EU!) immigration stuff that stuck. As witnessed by the 'overwhelming majority' who voted to <insert single, simplistic reason of the day here, according to who the speaker is>... All of which is total bollocks, pardon my Esperanto....
1 Not that a country would ever blanket ban another country's population from engaging in everyday international travel, above and beyond and actual individual/organisational membership of a persona non grata list... Oh, wait!