The schemes include a new "transport hub" in Scarborough and a new car park and footbridge in Seamer.
If the bid is successful the authority said it hopes to start work by the end of March 2023.
Well-known Scarborough musician to open new Yorkshire music school
Surf instructor helps RNLI rescue four people who drifted out to sea on inflatable mattress in Scarborough's North Bay
Scarborough woman robbed elderly woman of her walking sticks - then tried to snatch walking stick from elderly man minutes later
Whitby Regatta 2022 - all the pictures from the rowing presentation evening
Seafret shrouds Scarborough for two days while rest of coast basks in sunshine
The £8.4m plan at Scarborough railway station is to create a transport hub to regenerate the area and strengthen connections between the station and town centre as part of a wider 'gateway' scheme which is led by Scarborough Council.
The authority's ambition is to radically improve the area around the railway station to create a more attractive entry into Scarborough for visitors and residents.
The road junction and public space would be remodelled as a 'station square' to make it easier to access the town centre from the station and to boost its visual appeal.
A new transport interchange would be created to provide more opportunities for people to travel around the area and leave their cars at home.
The proposals include electric vehicle rental facilities and charging points, cycle storage, hire, repair and amenities, bus stands and waiting areas, taxi booking stands, and commercial space.
Cllr Keane Duncan, the executive member for highways and transportation, said the authority is committed to modernising North Yorkshire's transport infrastructure.
"The bids demonstrate the council's ambitions to improve our stations, connecting residents with employment and supporting economic growth," he added.
A £25.2m project at Seamer station would provide a new pedestrian and cycle link connecting the station to residential sites in the west, a new three-span open footbridge across the rail line and A64, including lifts to platforms one and two, and a new station car park to the east of the track on to the A64.
Mining company Anglo American, whose head office of its Crop Nutrients business is in Eastfield, has announced its support of the Seamer development.
Matt Parsons, General Manager of External Affairs, said: "The current station is in real need of an upgrade.
"In addition to our own business needs, Eastfield is the key growth area for the wider borough and improvements to Seamer station are essential to support future development.
"If we want to attract more businesses to invest and people to live in the area, the improvement of Seamer station is paramount."