When I was in a biochemistry lab and looking for the promoter in front of a (human) gene of interest I started by downloading the sequence from UCSC Genome Browser (https://genome.ucsc.edu/). There are options to download at least 2kb in front of the transcription start site (TSS). I then looked for the TSS (if you save the file where exons are in all caps this should help).
Most mammalian promoters have a TATA box (consensus sequence 5'-TATA(A/T)A(A/T)-3') close to the TSS. This is where the core promoter is.
You can then look to see if there is previously published papers on your gene of interest which may list some transcription factors that activate your gene of interest.
If you look up those transcription factors you should be able to find a core binding sequence which you can then search in the sequence you downloaded from UCSC.
It's a lot of work and there may be more online resources (gene-regulation.com ?) that are more plug and play but when I annotated the promoter myself I was much more confident that the sites I was finding were real.
as christopher said go to the UCSC website. just select your species and assembly and type the gene name of interest. you'll reach a browser with lot of options, including regulation options.... but you can also choose arbitrarily the position you'll want. at the top of the page, you'll have a "view" page and DNA you'll have. in the genome browser, you can also click on the gene and you'll have enough stuff to do your analysis. take some times in this website, there are some interesting tools and remember that all that you can see in the genome browser you can have as files in the table browser.
Actually most papers I read they have the promoter region of human , and I am using mouse , and I don't know if they are the same or no since I don't know how to search for the promoter.
most of promotors, in human or in mouse, are composed of about 100Bp but you can explore to 500. in fact you can find promotors away from the genes at 200-400 Kb. just to be sure since now you'll have the sequences, try this site and get all transcription factors sequence in it (http://bioinfo.lifl.fr/tfm-explorer/tfm-explorer.php).
Looking upstream of the mapped transcript is the way to go. However, if your gene has several alternative transcripts then information about their expression (presence of CAGE tags). You may further compare the mouse and human transcripts and try to locate the positions of their exons.
We provide homology groups of transcripts and the identification of homologous promoters.
The great thing about mouse genes is that most of the transcription factors that activate your gene in humans will be conserved in mice. I think it's reasonable to expect 90% of the transcription factors that bind in humans also bind in mice.
Knowing where a promoter ends is a whole other story. I remember the gene I was looking at had a FoxA2 binding site almost 1kb away from the TSS. But there was debate weather it was active or not.
Depending on what you are doing with the promoter isolating the core promoter from insilico data may be reasonable or you may want more upstream sequence and do some type of biochemical validation of targets. But Fred is right. Plugging it in to tfm-explorer is a good first step.