Before you start cutting, be aware that you are dealing with load- bearing walls. Even non-load-bearing can cost $2500-$3000 to tear down, you need to replace the flooring, move electrical, etc. Load-bearing can cost $10000 for a one-story, or $20000-$30000 for a two story, so before you get out your hacksaw or sledgehammer, consult with both a structural engineer and your banker. (Costs are from Houzz.)

Yes are very correct! I would like to find an alternate for this space that would be both appeasing to the eye and affordable.

If you are allowed to transform the area into an open concept design you should be able to add plenty of space and room for furniture to make your breakfast area appealing and logical.