Electricians can be ingenious about where they find places to hide cables. (Behind or under skirting boards for example.) If a route is not available and running conduit outside isn't feasible, there's an option to run conduit "inside" through somethings called "cable trunking." Essentially it's a plastic box with a removable lid (like long thin tupperware) which (for the smaller cross sections) can be surface mounted and then the cables route therein. It's certainly "visible" but looks a lot neater than clipping a bare cable to the doorframes, skirting boards etc. However, you may well need to consider "domestic harmony" if contemplating this option and make sure "conversations" have been had in advance. Things that I don't regard as a "big deal" can be perceived as "the end of the world" by other people.
If you opt to run UTP cables, AVF mantra is to "always run two (or more)" along any given cable route. It is highly unlikely that a UTP cable will fail in service, but if one does and you have no alternate in situ, then you are off the air until you rip and replace. With an alternate in situ, you stand a fighting chance of getting back up again more quickly and it's surprising how often one can find a use for "just one more" later on. Cable is cheap compared to the hassle of installing it - the additional materials cost is not that large compared to what you'll be paying for the labour (for example.)
Finally just a quick word about your electrician. Ignoring the cowboys, most are fine people who do a great job of plying their trade competently and will willingly run in some UTP for you. However, a lot of the guys who are used to doing "domestic" work on thing like mains electricity or running in a bell wire or whatever are not aware of the additional stipulations and working practices required to install data networking infrastructure. Much less have the (rather expensive) kit needed to test and certify the work. It's not for nothing that there are specialist companies that guys such as I (professional network manager) hire in to do the work (with prices to match!) in our "day job." So, in the nicest possible way, you might care to try and get a feel for what you electrician's experience is of data networking.
I like to believe/hope that more and more domestic sparkies will be "standing up" their expertise and ability to install UTP to standards, not least because it will be a "nice little earner" for them alongside their other business.
There's a few people who regularly contribute to this forum that sound like they make a living doing this sort of work.
