Residential neighborhoods are much harder to operate a restaurant out of, but i'm guessing you have figured this out.
Are you just a sushi place or do you do other food? This will help with future advice.
Here are a few general tips:
To increase lunch sales - you have to market to those in your area most likely to eat out for lunch. That is not going to be the neighborhood's residents, they are all at school / daycare / work, your customers for lunch are going to be those that work in the area. Think police outreach centers, fire halls, day care centers, recreation facility workers, city offices, city maintenance properties, home business, medical clinics, school teachers and general shopping stores. These people will only have 30-60 minutes for lunch and don't want to travel for most of that time. Target your flyers and advertising to them. Make call-ahead and pickup lunches available. Make gourmet bagged lunches / platters etc. don't make them wade through a huge list of available options. 4-5 combos is enough but make them interesting and also offer an office combo something that serves 6-10 people that workers can buy to treat the office on a whim.
Find out who the predominant employer in your residential area is - then approach them about specials or even bringing bagged food from the restaurant to their workplace. BENTO BOXES! you could make a killing by offering these to your local neighborhood workers. You'll want to talk to the HR people or VP etc. Make it a no loss situation for them. Take a decent amount of food - but you should expect to run out - this way there is no waste for you, also have a method for those that missed out on your gourmet food to 'pre-order' next time. The pre-order increases the accuracy of how much you need to prepare and makes the customer feels special. Don't do everything a'la carte... too many options - make a few themed choices and most will buy them. Don't ever refuse a'la carte or special orders just make it simple for those new to sushi.
Be flexible with the food you offer - sushi might be a hard sell depending on the demographics of your area. Offer alternatives that fit into the same niche you're trying to fill. ie. more makizushi - chirashizushi - tempura - pickled foods - milk toast sandwiches - rice bowls with simple sweet and sour or tonkatsu proteins.
Don't expect people to know or understand sushi - make things simple for them. Offer family sampler platters, individual combo's and dinner for 3, 4, 5 or 6 menu's.
For evening meals - you need to make yourself 'a destination' ensure ample parking (make a deal with a local lot or pay for the meters... one place I worked at we sent the bus-boy out to plug change into the meters in front of our place every 2 hours... then advertised it's always free parking in front of the place).
Quick service, these rich demographic types you refer too are also the busiest they have a billion lessons / groups / events etc. either take-out or eat in it has to be fast... this works in your favor as you can turn tables faster. In the door - drinks in 1 minute after seating (if they can't decide that fast put water down and come back), apps in 5, food in 15 and out the door in 30-40. Advertise it as such - quick, wholesome, gourmet, upscale, farm-to-table, sustainable, fresh, organic, and yummy food for your family in less than 3/4 of an hour!
Your focus should be on the neighborhood residents on Fri-Sat-Sun... other days the focus should be on the workers in your area. Find out when the predominant work-force gets off work, then make a "take-it-home" with you special for them for evening meals.
One last thing - advertising directly to 'families' seldom works... forget about flyers in their mail box etc.
Families go out to dinner based on word of mouth - personal recommendations - these are made from friends that they have at .... work / school / playgroups / lessons.
Rather than putting a few hundred flyers in the mail-boxes of those that live in the neighborhood - put those flyers into the places that they work / school / play etc.
Most home flyers end up being floor covering around the cat litter box - that is if they are opened out flat. Often they go unread straight to the trash.
I have more advice but this post is long enough and I need more information from you!