Well it all depends on your personal taste and what you deem to be classy and elevated.
You've had some really good responses but just to reiterate and add some of my own I've not seen I would;
Declutter - 110% !!
Spotlessly tidy and smelling fresh at every viewing -scented candles, open windows before (providing you don't live near anything smelly!), essential oil based cleaners are nice for leaving a lasting smell purdy and fig are good.
Fresh flowers or healthy plants in a couple of appropriate places - good quality ones
Lights and lamps all on
Heating on to cosey levels in autumn/winter/spring
Before this though I would;
Fix any major and minor maintenance issues - de-mould bathroom grouting and sealant, reseal if necessary, make sure doors don't stick, look at any cracks in the plaster - get them filled and painted
Hide/get rid of any broken furniture
get a Flash magic eraser and go round and give any scrapes on your paint a good buff and clean - same with wood floors if you have
repaint if rooms are looking really tired
Look at your paint choices - anything wild or really specific think about going neutral, if you have any of the dark Farrow and ball esque blues they can probably stay but anything else pick a nice warm neutral / off white - not a grey
Consider white bedding and make sure it's clean on for every viewing
Also think about your garden / outside of your property, again fix any big projects small maintenance issues. Remember curb appeal.
Make sure your gate if you have one is clean and works/doesn't stick.
Consider having upvc cleaned or if you have wood framed windows painted if they are looking tired/flakey
Grass cut, garden tidy - any plants and trees cut back and neat, get rid of anything which looks dead!!! If you're on the market at the mo consider brightening up a dull winter garden with some spring bulbs.
Have a look at the roof - of you're in an area where moss collects consider having it cleaned
Go round with a leaf vac before viewings.