I stayed at home and went to my local uni (RG and one of the best in the country for my subject). This was 15 years ago now, so just before fees came in and the last year of maintenance grants. I had applied and got offers from unis all around the country, but was persuaded by my parents to stay at home and commute, primarily because they were worried about me coping financially and having to work and study etc. In addition they were unable to provide any financial contribution, but could afford to have me continue living at home.
Yes, staying at home made things easy in some ways (Mum still cooked for me, etc., I didn't have to deal with bills other than personal expenses) but was hard in others and certainly by the time I was at the end of my second year I was chaffing at the bit somewhat.
I basically had no social life because I missed out on all the getting to know people stuff that happens plus the kind of enforced socialisation that happens when you have a load of 18/19/20 year olds all moving away from home to live in halls for the first time. I am a naturally shy person, so it was easy for me to become isolated and because I commuted in daily I kind of slipped by most peoples radar - I don't think I could tell you the name of anyone on doing the same modules as me for all of the first year at least. Looking back, had I gone away and been in halls I would have had to join in (and it would have been easyfor me to do so even given my shyness, just by the nature of everyone being in the same situation).
As it was I basically went to lectures and came home/went to the library to work and missed all the other uni experiences completely - which I feel has had an ongoing influence in my life since tbh.
Whilst it may sound all doom and gloom I do need to add that I did meet my wonderful DH during my second year (been together 12 years, married 4 years next month with 1 DC and 1 on the way).
Financially, bear in mind no fees to pay 15 years ago, I managed during term time with my loan & grant and I worked (supposedly part-time, more like full-time 6 days a week) during the summer holidays between years 1&2 and 2&3 which paid for various other things like getting to interviews in year 3, clothes and a couple of things like a new PC, etc.
Post-university, I moved hundreds of miles away and whilst I coped fine, I had to learn to deal with household things like bills and generally running a household while getting to grips with working full-time. My peers who had moved away for Uni got to learn about those thing then, within a slightly more relaxed envionment with lots of other people in the same boat.
My sister also stayed home and went to the same Uni - she had a similar experience, though she was slightly more social. Also, a number of her school friends did like wise (my friends all went away to Uni) - so they continued to socialise.
This has turned into a bit of a mega essay I'm afraid but I wanted to tell you my experience. If, when the time comes, my DC wanted to go to their local Uni (which given where we live is entirely possible), I have to say that I would suggest that they think long and hard about whether it was the right thing to do. At the very least, I would try to encourage them to move into halls for the first year.