The station in the Hampshire town of Hythe (Wikipedia) closed in 1966 when passenger services on the Fawley branch line from Totton (a.k.a. Waterside Line) were withdrawn. The former station building now houses the Waterside Heritage Centre.

Three Rivers Rail Partnership is the promoter of a scheme to reopen the Waterside Line. The proposed southern terminus is a new station called Hythe & Fawley Parkway and further stations at Marchwood and Hythe Town are included in the scheme.

Waterside Line. Map source: Three Rivers Rail Partnership

Map source: Bringing Passenger Trains Back to the Waterside (pdf), Three Rivers Community Rail Partnership.
Three Rivers Rail Partnership – Network Map

Map source: Bringing Passenger Trains Back to the Waterside (pdf), Three Rivers Rail Partnership.
Location of former Hythe station

© OpenStreetMap contributors | OpenStreetMap copyright notice | View context map of proposed location
We do not yet know the location of the proposed Hythe Town station. Looking at the map and considering the distance between Hythe town centre and the unconfirmed Hythe & Fawley Parkway site, we think School Road is the most likely location.

Proposed stations on a reopened Waterside Line

Marchwood

Hythe Town

Hythe & Fawley Parkway

Read more about the Waterside Line reopening scheme

Further reading

Fawley branch line – Wikipedia

Hythe, on Disused Stations website

Hythe railway station (Hampshire) – Wikipedia