Tokyo - Hakone, Romance Car vs Shinkansen

I really want to ride the Shinkansen and a day trip to Hakone will be my only chance, but to save money I'm going to take it one way and the Romance Car the other way. Going to Hakone will be daytime and leaving will be nighttime, so my question is

Does either route have a better view at day/night?

You cannot see anything at night/after sun sets, except for city lights and the internal train illumination.

The night view along the route from Tokyo to Hakone is not as beautiful as it in daytime. The most popular attractions in Hakone are Hakone Onsen, Hakone Shrine, Lake Ashinoko, Owkudani,etc. They all deserve a visit. BTW, since you are travelling in Japan, I recommend you use Tourank app. It's a smart mobile travel guide for Japan.

Get the train in the morning as it gets you to Odawara quickly (and you can stop off at the castle if you wanted). The local train to Hakone (and/or getting the "free pass" is easy to do at the station as well.)

I really want to ride the Shinkansen
but to save money I'm going to take it one way and the Romance Car the other way.

When your seat is not reserved, logically you can take a Tokaido Shinkansen train at less than 2000 yen for about 5 to 20 minutes.

Concerning specific short sections of Tokaido Shinkansen, surcharges for rides without seat reservation are set at especially low prices.

By the way, Shinkansen trains do not bring you as far as to Hakone; you can make a transfer in Odawara between JR Tokaido Shinkansen and Hakone Tozan Railway.

When will you travel?

Shinagawa/Tokyo to Odawara is 3050 for a unreserved seat. Trip takes 25/30 minutes.

Shinjuku to Yamato-Hakone is half that cost and takes about 90 minutes.

Both views are pretty unexciting between Tokyo central area and Odawara on both options.

I'd probably go the quicker option n the morning so you can get started early. Use the slower option for rest and returning.