we're doing our wedding for around 3k... not including honeymoon. i was extremely stressing out because we live in los angeles, where everything is twice is much - not kidding.
eventually we settled on a reception at a hall at our university's campus... it's a gorgeous building, and because we're students there, we get it for $350, all day, everything included. we couldn't pass that up, despite our initial dislike of getting married on campus.
my advice is to focus on one aspect that's really important to you, and spend the most money/attention on that. that could be invitations/programs/paper goods, favors, attire, food, cake, music, photography, etc. we chose to skip music, found a cheap photographer, and i'm DIYing invites for around $150 in exchange for offering more food options at the reception.
think of unique places to get married - museums, backyards, parks. chances are, if it's a random place, they haven't dealt with many weddings. that means they probably won't be as organized, but it also means they'll be cheaper.
as far as alcohol, it's only worth including if you're at a private place (residence). otherwise, it adds a LOT of money!