I suggest some serious browsing on Etsy for reasonably priced large canvases.

https://www.etsy.com/listing/199708042/large-abstract-painting-original?ga_order=most_relevant&ga_search_type=all&ga_view_type=gallery&ga_search_query=large%20abstract%20painting&ref=sr_gallery_14

On one wall in the dining area I would hang a large mirror- then add sconces or framed prints on each side- across from it I would hang a large canvas print ( this one from Wayfair.com) or see if you can find a huge one at a thrift store you like- Also a console table under the mirror ( or print) would be nice.

You can also go online and look at poster prints and get two framed for one of the walls. Lots of choices out there.

Tailored to where you are -- or want to be, but you get the idea, maybe mounted or with less of a visible frame...

Long Island Gradient Triptych · More Info

Lord Bodner Octopus Triptych Print, Forest Green/Off-White, 40"x32" · More Info

"Woodland Mist Triptych" Limited Edition by Scott J. Menaul, 57x36 · More Info

Tunnel Of Trees Print Triptych Wall Art · More Info

I'd go for a big painting. Maybe a console or buffet under it. All of these are from etsy.com. There are a few good artists mixed in with the schlock art.

Or look at Grandin Road or Pottery Barn. Two examples of those sites.

Don't do lots of small pictures especially photos.

Your tile is fabulous!!!

www.saatchiart.com is another great art site

there are also giant wallstickers, all different types, mixed with your photos, can be quite impressive and your originality

kitchen · More Info

found these on etsy. 2 can make quite a statement. using your best serving dishes, what you find on trips antique stores tj maxx etc.

glass etagere – Etsy · More Info

#ImpactOfDesign · More Info

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i would prefer anything creative by you or an original to a print

Your display cabinet on above wall is not big enough for wall.

Consider large 'found objects' like interesting doors or gates etc.

Or you can use these molded paper 3D panels and mount them in any configuation on the wall. It's $62 for a set of 10 panels and you can paint them any color.

http://inhabitliving.com/collections/wall-flats-3d-decorative-wall-panels/products/hive-wall-flats-3d-wall-panels

I can't afford large art either so I 'duplicate' what I like. Here's a painting I liked and I copied it on two large canvas frames.

Here are some other inspirational options.

WOW! So many awesome ideas - thanks!. I'm held back a little by the busy-ness of the tile. The one wall closest (not opposite) the tile is the biggest blank slate, and there isn't really room for furniture there because of the island clearance. The wall behind the dining table is easier - yes, the bookshelf there is only temporary...

BeverlyFLADeziner I LOVE the wall flats. I think they may be too busy in the kitchen but would be so cool somewhere else. Now I have to find a place!

Wall in hotel in Far East with cast bronze wall climbers.

These smaller cast images are from Global Views and can be purchased on Amazon

You can purchase a large map for the wall like the one below

This large paper mural is available from Anthropologie

cfweber- your tiles are far enough away that they shouldn't compete with art on these walls. Just don't over do! :)

Have thought about using some of our own photos (these from Greece) - maybe three large prints would be cool...

How about a large poster print of a map of greece, you could hand color, parts important to you and then put your pics with it.

I think you could do a fake plant(or really--pic is a fiddle leaf fig) in the corner and a set of framed art on the wall. Also you could do a large square canvas on the main wall in the kitchen. If you are looking for contemporary abstract feel free to check out my art and email if you have questions.

Love an art challenge! You already have a ton of ideas to consider cfweber but keeping it modern is key. We create bespoke artworks of a variety of styles on plexiglas which would certainly suit your modern style, if not your remaining budget! Here's just a couple of examples, but feel free to browse our signarture online gallery to find something that suits your personal taste if the idea appeals. We ship worldwide.

If you choose to go with your own photos, do consider mounting then to plexiglas. The material really brings out the depth of colour and the frameless presentation is a very clean, modern look.

signarture ‘islington’ perspex plexiglass artwork · More Info

signarture 'burrawang' perspex plexiglas artwork · More Info

You know what else you might like to do? Do a color bloc for your pics, you could even do it in the shape of the steeple, arch, or the 5 bell openings, in the color of the water. Which each pic housed in white, or the other way around.

Hollywood Regency Living Room · More Info

The Capistrano - Quail West · More Info

The art you choose should speak to you. It has to be what you love.
As for placement you already have small framed photos on bookshelves and tables. I would go for a few large statement pieces, but I would not make them perfectly symmetrical. I would use a large piece and 2 or 3 smaller pieces on the completely bare wall and then use something complementary in a medium/large size on the other wall and get a tall vase with flowers or another standing piece of art for on the side table has the same colors to provide balance on that wall.
I would go with simple frames or frame-less canvases.

https://www.etsy.com/shop/dgalerie?ref=hdr_shop_menu