Vilnius on budget / must sees?

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Going for four nights, next week, so three whole days, staying in the old town
Me and DP, but friends who live about an hour away will join us some of time or at least for a night or two out (or eating at our airBnB anyway)
We don't have much spending money and also are vegetarians, as far as I know there's just one vegetarian restaurant, as we are skint anyway I wonder if we should just stick to local bakeries/ supermarket?
What are must haves to see? I love photography and we both are happy to see as much as can on foot or by train
Also what clothes to pack for this time of year for sightseeing? A full on winter coat or just a light jacket?

I do definitely want to see the Gates of Dawn and the Literati Street.
Also is it worth travelling out to the nearest seaside? I've never seen the Baltic sea.

Vilnius is lovely and good value. Lots of lovely churches, little streets, cathedral, palace, hill with three crosses, uzupis - so plenty of wandering around for free. This museum was very good
www.tripadvisor.com/Attraction_Review-g274951-d284404-Reviews-KGB_Museum_Genocido_Auku_Muziejus-Vilnius_Vilnius_County.html
I also went to a couple of exhibitions in the palace - paid about 6 euros total I think. I stayed in the centre of town and there were lots of bakeries and a couple of small supermarkets selling nice fruit, rolls etc so easy to make your own sandwiches or a snack for lunch.
I took a day trip to trakai castle and the paneriai memorial park - both very interesting.

*It was about 5 years since last went and the veggie restau6was great.
The TV tower was ok for something to do
See if you can find the Frank Zappa bust!!

Hair just started editing and the post got posted. The veggie restaurant was good so hopefully that is the same.
There is a bust of Frank Zappa in the most unlikely place. We made a point ,of finding it!!!

There is more than one vegetarian restaurant, eg: Rosehip Bistro, Vegafe, Radharane, Casa La Familia Pizza, etc..

www.happycow.net/europe/lithuania/vilnius/

The restaurants look great! It looks like things have improved since I was last there.
I really fancy going back!