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It's possible to walk up through olive groves from the centre of the village - but from Romanza it makes more sense to go to Avliotes. If the traffic worries you, you can hop on a bus. Get off in Avliotes and walk down from the village square about 100 yards. There's a little, very quiet, road that goes steeply down to the left. That leads to Peroulades and Logos Beach, where there's a very nice bar, restaurant and viewing area. It's a lovely walk. If you're adventurous you can continue from Peroulades on to Sidari, and get a bus back from there.
Alternatively, walk back to Avliotes and have a nice lunch or beer in Ilios taverna, which is open all year and mostly patronised by locals, so it's very authentic and not tourist modified.
From Avliotes you can walk down through the olive groves and emerge near Sliver Moon. That's a great walk, but wear good walking shows. We saw one woman attempt it in flip-flops. and she was in tears by the time she made it to the bottom.
If you are fit, another good walk is to Afionas - over the ridge to Arillas and then a long climb to the beautiful village that superb views from high over Arillas, St George's and the islands.
I can give you more details if you want.