The fireplace was never a big deal to me, but we live in CA near the coast. That’s where I would save money. No fireplace, no odd wall indentations (extra drywall cost), no venting, no surround or mantels, no electricity or gas plumbing needed. 
I’d plough the savings into a 70-80" screen TV with surround sound system. Or other areas.
I feel like we will probably keep a fireplace since we are in a rustic cold weather climate. It could come in handy with a power outage.
I hope our resident remodel pro @coralbrook will be back soon and will chime in with her cost cutting suggestions! She is a master of finding deals. 
If that’s a worry, then I’d look into planning and installing backup power generation. That could be $10,000 +/-, depending on size and installation.
We have had both wood/gas fireplaces. We would be ok with either but if allowed my H was leaning toward wood burning. We will be in a rustic area.
When we partially refreshed the insides of our House2, I looked for deals on light fixtures and sinks and whatnot on Amazon, HD (avoiding contractor grade stuff!), Costco, and manufactures’ websites. For example, the open box light fixture I got for our dining room is quite cool and only cost a fraction of the new one’s cost. It took time and some web surfing effort to assemble this stuff piecemeal, but I think we saved quite a few $$.
I’m not sure if a power outage is a big concern. We will have city electric/underground utilities. A cozy fire seems like a good idea on occasion.
Photo please?
It looks like this:
We are a family of chemistry nerds, so it fit us perfectly! 
You might not like it.
Another cost saving tip: do as much work yourself as possible. Anything that is not required to be installed by a pro and inspected is fair game. Like painting the siding.
I’m a huge fireplace fan! I love the architectural interest and focal point it provides in a room and if your home is located in a more northern locale I’d include at least one or two in the budget 
. It’s so cozy and wonderful to sit by a fire.
I don’t mind a tv above a fireplace. But I don’t love the tilted look. But also I don’t like a tv on a stand as an afterthought. I prefer a tv mounted…somewhere. You can also get the framed tv’s - so it doesn’t look like a tv when it’s not on.
I agree that a lake house kind of screams fireplace to me and not having one at that kind of property might hurt resale down the line. But does your family use its fireplace now? I’ve been in many places where our family wanted a fireplace, but we never actually lit one (even the gas insert kind). But if you’d use it, it’s definitely a good thing.
As far as ways to save on costs, skip accent tile. Accent tile material is usually more expensive, and it adds extra labor costs for installation. But mostly, because accent tile is usually one of the things that will date a kitchen or bathroom most quickly. As a general tip (thanks to Maria Killam!) if you choose to get a patterned tile, know that it is going to be setting up a permanent color scheme (so if it’s a multi-hued beige or grey tile, those colors will now be part of your decor for the duration of their installation). Plain colored tiles leave lots of room for changing decor preferences and they are usually more affordable than their multi-colored brethren.
As @1dadinNC mentioned, box shapes are your friend. But also, the more corners there are, the more expensive things become (i.e. if the building has lots of carve outs and peninsulas sticking out, even if they’re also 90 degree angles, that will increase the cost of the building).
You don’t need to pay for the most expensive, exotic wood floors either. Choose a species of wood that you find attractive and will hold up well, and shoot for a timeless stain color (medium brown being my favorite, but if you like lighter colors, then blonde also works).
Some things might also be easier to have wired/plumbed and then other portions installed later. For instance, maybe running the necessary elements for the sauna (electric/plumbing) before the walls are put up, but then installing a sauna down the road when money is more available.
A powder room can be nice, but doesn’t need to have tile anywhere but the floor especially if your sink has an integrated backsplash. You could go for high end vinyl floor tiles, but I doubt the savings would be that much for a small space.
Design the house and space for the cloudiest winter day. It’s always great in the summer but on the worst winter day, light is key.
We live in the upper Midwest. Our power lines are buried but we have a well. When the power goes out, so does the water. The good news is because the power lines are buried, we are a priority to get back online because an outage affects more homes. It’s never been off long enough even in the winter for us to worry about the heat. Flushing the toilets is another story…
We have a gas fireplace but my sil had a wood burning one at her cottage and it was a centerpiece of the house.
The best thing about our house are the best windows and extra insulation. I can sit next to my windows and it’s warm even on the coldest winter day.
Ideas to save, use stock cabinets, stock hardware, inexpensive lighting fixtures. Nothing custom. Build great bones and the other stuff can be changed with time
LOL. We have a fireplace and very rarely use it but I still like it. It just adds a certain cozy ambiance. I put a big basket of flowers in it during spring. I also have big candles that I put in it at other times.
I definitely do NOT like a TV over the fireplace. Total pain in the neck even if it’s far away. It’s much nicer to be able to decorate a mantle or have a wreath over the fireplace.
Doesn’t seem like money saving tip but don’t skimp on good insulated windows. Well worth it.
Lighting can be really expensive. Order your own from online sites. Same with plumbing fixtures. Outlet tile/flooring places can save you a lot especially if you have smaller areas to fill.
I have a wood burning fireplace but am considering converting to a gas insert. I love the ambiance but not dealing with the wood and ash.
I keep it filled with flame less candles most of the year since I’m in the south. Just a push of the remote and it’s glowing with candle light. 
In the south also. If I did it again it would be gas. I also use flameless candles sometimes or just put in votives which burn out on their own. Just something about a fireplace that makes me happy!
Make sure you ask your builder if he has any discounted vendor relationships that you can tie into. Our builder put us in touch with his bath person and we were able to get everything at his cost. It was cheaper than anything else we could find of the same quality. Same with flooring.
I have all lower drawers, of different depths for different purposes (e.g. I have my dishes in drawers next to my dishwasher) and I personally prefer them over doors fronting pull-outs myself.
But no matter what - either of those options over lower cabinets any day, the storage is so much easier!
