Beth there are 2 other budget/moderate places on Theotokopolou street to consider ... they are THE absolute closest to the seafront, they face each other across the lane at the very end, just before the ramp you walk down, to the parking lots & waters edge.
One is called "hotel Hera Studios " on the RH side facing seaward... it really has 3 units. It doesn't have its own website any more, but here's the link on Booking.com, with good photos of the views from its balconies .... interesting, isn't it, when a place does NOT have good views, they always have lots of photos of the bathroom towels & bed pillows! This place can show views from all 3 units. One has a kitchenette, I think the others have (besides fridge) coffeepot & electric hotplates & sink .... the basics for breakfast. I've sent several people here who were happy with it.
The other is Casa di Pietra... a "townhouse" with Ithink, 5 rooms. http://www.casadipietra.gr -- The front room has 3 singles... 2 single beds together & one on the side. Big French door/windows to the front... there's also a double big windows facing rear. As website shows (which hasn't changed for years), it has no "decor" but probably since I stayed there it's added an amenity like an electric coffeepot. It's owned by a great guy named Josef. His desk is in the back of lobby and he has a little cask of wine on top of it -- he owns vineyards & offered us sips of the latest. I recommended the place to others, then 2 yrs later I came with 2 other people but stayed across the way at Palazzo Hotel. We were on our way to stay at Falassarna and I stopped by just to say HI, and Josef insisted on giving me a bottle of his wine to drink at sunset... and we had such a memorabl sip & sunset, such a nice man! You would book it by going direct to him... and he'll respond with details. I don't think he does booking.com or other such.